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Use of Statistical Tools – CBSE NCERT Study Resources

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11th

11th - Economics

Use of Statistical Tools

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Overview of the Chapter

This chapter introduces students to the fundamental concepts and techniques of using statistical tools in Economics. It covers the importance of data collection, organization, presentation, and analysis to draw meaningful conclusions in economic studies. The chapter emphasizes practical applications of statistical methods to interpret economic phenomena.

Statistical Tools: Techniques used to collect, analyze, interpret, and present data systematically for decision-making in Economics.

Key Concepts

1. Data Collection

Data collection is the first step in statistical analysis. It involves gathering relevant information from primary or secondary sources to study economic issues.

Primary Data: Data collected firsthand by the researcher through surveys, interviews, or experiments.

Secondary Data: Data obtained from existing sources like government reports, journals, or published studies.

2. Data Organization

After collection, data must be organized systematically for analysis. This includes:

  • Classification: Grouping data into categories based on characteristics.
  • Tabulation: Presenting data in tables for clarity.

3. Data Presentation

Data can be presented visually using graphs, charts, and diagrams to make patterns and trends easily understandable. Common methods include:

  • Bar Graphs
  • Pie Charts
  • Histograms
  • Line Graphs

4. Measures of Central Tendency

These are statistical tools to identify the central or typical value in a dataset. The key measures are:

  • Mean: Average of all values.
  • Median: Middle value when data is arranged in order.
  • Mode: Most frequently occurring value.

Central Tendency: A single value that represents the center of a data distribution.

5. Measures of Dispersion

Dispersion measures how spread out the data is. Common tools include:

  • Range: Difference between the highest and lowest values.
  • Variance: Average of squared deviations from the mean.
  • Standard Deviation: Square root of variance, indicating data spread.

Applications in Economics

Statistical tools are widely used in Economics for:

  • Analyzing market trends.
  • Forecasting economic growth.
  • Evaluating policy impacts.
  • Conducting consumer behavior studies.

Conclusion

This chapter equips students with essential statistical techniques to analyze economic data effectively. Mastery of these tools helps in making informed decisions and understanding complex economic scenarios.

All Question Types with Solutions – CBSE Exam Pattern

Explore a complete set of CBSE-style questions with detailed solutions, categorized by marks and question types. Ideal for exam preparation, revision and practice.

Very Short Answer (1 Mark) – with Solutions (CBSE Pattern)

These are 1-mark questions requiring direct, concise answers. Ideal for quick recall and concept clarity.

Question 1:
Define primary data in statistics.
Answer:
Definition: Data collected firsthand for a specific purpose.
Question 2:
What is the range of a data set?
Answer:
Difference between the highest and lowest values.
Question 3:
Name one measure of central tendency.
Answer:
  • Mean
Question 4:
What does standard deviation indicate?
Answer:

Dispersion of data points from the mean.

Question 5:
Give an example of secondary data.
Answer:
Government census reports.
Question 6:
What is class interval in grouped data?
Answer:
Definition: Range of values grouped together.
Question 7:
Which graph represents time-series data?
Answer:
Line graph.
Question 8:
What is the mode of 2, 3, 3, 5?
Answer:
3.
Question 9:
Define correlation in statistics.
Answer:

Relationship between two variables.

Question 10:
What is a histogram used for?
Answer:
Displaying frequency distribution of continuous data.
Question 11:
Name one sampling method.
Answer:
  • Random sampling
Question 12:
What does CPI stand for?
Answer:
Consumer Price Index.
Question 13:
Give an example of qualitative data.
Answer:
Survey responses on customer satisfaction.
Question 14:
What is the median of 7, 9, 12?
Answer:
9.
Question 15:
What is the purpose of a pictogram in data representation?
Answer:

A pictogram uses pictures or symbols to represent data, making it visually appealing and easier to understand for non-technical audiences.

Question 16:
Name any two measures of central tendency.
Answer:

The two common measures of central tendency are:
Mean (average)
Median (middle value)

Question 17:
What is the difference between discrete and continuous data?
Answer:

Discrete data takes specific values (e.g., number of students), while continuous data can take any value within a range (e.g., height, weight).

Question 18:
Why is random sampling important in statistical surveys?
Answer:

Random sampling ensures unbiased representation of the population, reducing errors and improving the reliability of results.

Question 19:
What does a histogram represent?
Answer:

A histogram is a bar graph showing the frequency distribution of continuous data, where bars touch each other to indicate intervals.

Question 20:
What is the formula for range in statistics?
Answer:

The range is calculated as:
Range = Maximum Value − Minimum Value
It measures the spread of data.

Question 21:
How is a pie chart useful in data presentation?
Answer:

A pie chart visually represents proportional data as slices of a circle, making it easy to compare parts of a whole.

Question 22:
What is the main limitation of using mean as a measure of central tendency?
Answer:

The mean is affected by extreme values (outliers), which can distort the average and misrepresent the data.

Question 23:
Define mode in statistics.
Answer:

The mode is the value that appears most frequently in a dataset. A dataset can have one, multiple, or no mode.

Question 24:
What is the purpose of standard deviation?
Answer:

Standard deviation measures the dispersion of data points from the mean, indicating how spread out the values are.

Very Short Answer (2 Marks) – with Solutions (CBSE Pattern)

These 2-mark questions test key concepts in a brief format. Answers are expected to be accurate and slightly descriptive.

Question 1:
What is the purpose of a histogram?
Answer:

A histogram is a graphical representation of data using bars to show the frequency distribution of continuous data. It helps visualize patterns, trends, and outliers in the dataset.

Question 2:
Explain the term measures of central tendency.
Answer:

Measures of central tendency are statistical tools (mean, median, mode) that identify the central or typical value in a dataset, summarizing its distribution.

Question 3:
What is the formula for calculating mean deviation?
Answer:

Mean Deviation = Σ|X - X̄| / N
Where:
X = Individual data points
X̄ = Mean of data
N = Number of observations

Question 4:
List two limitations of using secondary data.
Answer:
  • May not be fully relevant to the current research.
  • Risk of inaccuracy or bias if the source is unreliable.
Question 5:
What is the importance of sampling in statistical analysis?
Answer:

Sampling allows researchers to study a representative subset of a population, saving time and resources while providing accurate inferences about the whole group.

Question 6:
How is quartile deviation calculated?
Answer:

Quartile Deviation = (Q₃ - Q₁) / 2
Where:
Q₃ = Third quartile (75th percentile)
Q₁ = First quartile (25th percentile)

Question 7:
Name two graphical tools used to represent time series data.
Answer:
  • Line graph
  • Bar chart
Question 8:
What does a scatter diagram indicate?
Answer:

A scatter diagram plots paired data points to show the relationship or correlation between two variables. It helps identify trends, clusters, or outliers.

Short Answer (3 Marks) – with Solutions (CBSE Pattern)

These 3-mark questions require brief explanations and help assess understanding and application of concepts.

Question 1:
Explain the importance of measures of central tendency in statistical analysis with an example.
Answer:

Measures of central tendency like mean, median, and mode help summarize large datasets into a single value representing the center of the data. They provide a quick understanding of the data's typical value. For example, the mean income of a country helps policymakers assess average economic well-being, while the median identifies the middle value, reducing the impact of extreme values. These measures simplify comparisons and decision-making.

Question 2:
Differentiate between primary and secondary data with suitable examples.
Answer:

Primary data is collected firsthand for a specific purpose, ensuring accuracy and relevance. Example: A survey conducted by a researcher to study consumer preferences.
Secondary data is pre-existing data collected by others for different purposes. Example: Using government census data for economic analysis. Primary data is more reliable but time-consuming, while secondary data is cost-effective but may lack specificity.

Question 3:
Describe the steps involved in constructing a frequency distribution table from raw data.
Answer:

To construct a frequency distribution table:

  • Step 1: Identify the range (difference between highest and lowest values).
  • Step 2: Decide the number of classes (groups) and class width (range ÷ classes).
  • Step 3: Tally the data into respective classes.
  • Step 4: Count frequencies for each class.
  • Step 5: Present the table with class intervals and corresponding frequencies.
This organizes data for easier analysis.

Question 4:
What is the purpose of standard deviation in statistics? Illustrate with a simple calculation.
Answer:

Standard deviation measures the dispersion of data points from the mean, indicating variability. For example, consider data: 2, 4, 6.
Step 1: Calculate mean = (2+4+6)/3 = 4.
Step 2: Find deviations: (2-4)=-2, (4-4)=0, (6-4)=2.
Step 3: Square deviations: 4, 0, 4.
Step 4: Average squared deviations = (4+0+4)/3 ≈ 2.67.
Step 5: Square root ≈ 1.63. A low standard deviation shows data is close to the mean.

Question 5:
How does a histogram differ from a bar graph? Provide one use-case for each.
Answer:

A histogram represents continuous data with adjacent bars showing frequency distribution (e.g., height ranges of students).
A bar graph displays discrete categories with separate bars (e.g., sales of different products).
Use-case for histogram: Analyzing income distribution across age groups.
Use-case for bar graph: Comparing GDP growth rates of countries.

Question 6:
Explain the concept of correlation in statistics. Give an example of a positive and negative correlation.
Answer:

Correlation measures the relationship between two variables, ranging from -1 to +1.
Positive correlation: Both variables move in the same direction (e.g., education level and income).
Negative correlation: Variables move in opposite directions (e.g., price increase and demand decrease). Correlation does not imply causation but helps identify patterns.

Question 7:
Describe the steps involved in constructing a frequency distribution table for grouped data.
Answer:

Constructing a frequency distribution table involves:


1. Determine the range: Subtract the smallest value from the largest.
2. Decide the number of classes: Usually between 5-20.
3. Calculate class width: Range divided by number of classes.
4. Define class intervals: Ensure no overlap and cover all data.
5. Tally marks: Count frequencies for each class.
6. Summarize: Present classes and their frequencies in a table.

This organizes raw data into meaningful patterns for analysis.

Question 8:
What is the purpose of standard deviation? How does it differ from variance?
Answer:

Standard deviation measures the dispersion of data points from the mean, indicating variability. Variance is the square of standard deviation and represents average squared deviations.

Key difference: Standard deviation is in the same units as the data, making it easier to interpret, while variance is in squared units.

For example, if test scores have a standard deviation of 5, it means most scores are within 5 points of the mean, whereas variance would be 25, less intuitive.

Question 9:
Explain the concept of correlation with a real-life example. What does a correlation coefficient of +1 indicate?
Answer:

Correlation measures the strength and direction of the linear relationship between two variables, ranging from -1 to +1.

Example: Studying hours and exam scores often show a positive correlation—more study hours may lead to higher scores.

A coefficient of +1 indicates a perfect positive correlation, meaning both variables increase proportionally. For instance, if every additional hour of study increases the score by a fixed amount, the correlation would be +1.

Question 10:
How is a histogram different from a bar graph? Illustrate with an example.
Answer:

A histogram represents continuous data with adjacent bars showing frequency distribution, while a bar graph displays categorical data with separate bars.

  • Histogram example: Height ranges (e.g., 150-160 cm) with frequencies.
  • Bar graph example: Sales of different products (e.g., books, pens).

Histograms group data into intervals, whereas bar graphs compare distinct categories.

Long Answer (5 Marks) – with Solutions (CBSE Pattern)

These 5-mark questions are descriptive and require detailed, structured answers with proper explanation and examples.

Question 1:
Explain how measures of central tendency help economists analyze income distribution data. Provide examples.
Answer:
Theoretical Framework

Measures of central tendency like mean, median, and mode summarize data distributions. Our textbook shows they reveal income inequality patterns.

Evidence Analysis
  • Mean income in India (2023) was ₹1.72 lakh/year but skewed by top earners
  • Median income (₹89,000) better reflects typical earnings
Critical Evaluation

While mean calculates total average, median resists outlier distortion. Example: Kerala's median (₹1.12 lakh) vs. Delhi's mean (₹2.4 lakh) shows different stories.

Future Implications
Policymakers must combine multiple measures for accurate analysis.
Question 2:
Analyze the limitations of using correlation coefficients in economic forecasting with real-world cases.
Answer:
Theoretical Framework

Correlation measures (-1 to +1) show relationship strength between variables like GDP and education spending.

Evidence Analysis
  • India's literacy-GDP correlation (0.68) doesn't prove causation
  • Spurious correlation: Ice cream sales and drowning cases (+0.85)
Critical Evaluation

Our textbook warns that hidden variables (like summer heat) may influence results. Example: Stock market and monsoon correlation ignores global factors.

Future Implications
Economists must use regression analysis to test causality.
Question 3:
Compare primary vs secondary data collection methods using examples from recent economic surveys.
Answer:
Theoretical Framework

Primary data comes from direct collection (surveys), while secondary data uses existing sources like census reports.

Evidence Analysis
TypeExampleAccuracy
PrimaryNSSO household survey98% verified
SecondaryRBI annual report85% verified
Critical Evaluation

Primary data costs more but captures current realities. Example: PLFS 2022-23 unemployment rates (primary) differed from EPFO records (secondary).

Future Implications
Hybrid approaches yield most reliable results.
Question 4:
Demonstrate how index numbers simplify inflation analysis with WPI and CPI comparisons.
Answer:
Theoretical Framework

Index numbers convert complex price data into percentage changes. We studied base year (2012=100) comparisons.

Evidence Analysis
  • CPI (2023): 184.3 (food weight 39%)
  • WPI (2023): 151.7 (manufacturing 64%)
Critical Evaluation

CPI better reflects consumer impact while WPI tracks production costs. Example: 2022 onion price spike showed +15% CPI but +8% WPI.

Future Implications
RBI now uses CPI for monetary policy decisions.
Question 5:
Evaluate the effectiveness of time series graphs in presenting India's GDP growth (2018-2023).
Answer:
Theoretical Framework

Time series graphs plot quantitative data chronologically, showing trends like GDP fluctuations.

Evidence Analysis
  • 2018: 6.5% (steady rise)
  • 2020: -6.6% (COVID dip)
  • 2023: 7.2% (recovery)
Critical Evaluation

Graphs visually highlight the J-shaped recovery but mask sectoral differences. Example: [Diagram: GDP line graph with pandemic valley].

Future Implications
Complementary pie charts could show changing sector contributions.
Question 6:
Explain how measures of central tendency help economists analyze income distribution with real-world examples.
Answer:
Theoretical Framework

Measures of central tendency like mean, median, and mode summarize data distributions. Our textbook shows they reveal income inequality patterns.

Evidence Analysis
  • In India, the mean income (₹1.5 lakh/year) is skewed by top earners, while the median (₹75,000) reflects typical earnings.
  • Norway's mode income clusters around ₹9 lakh, showing equitable distribution.
Critical Evaluation

While mean is sensitive to outliers, median better represents skewed data like GDP per capita.

Future Implications

Policymakers use these tools to design progressive taxation, as seen in Scandinavian models.

Question 7:
Analyze the limitations of correlation coefficient in economic forecasting using 2023 inflation-unemployment data.
Answer:
Theoretical Framework

The correlation coefficient (-1 to +1) measures linear relationships. We studied how it fails to capture causality.

Evidence Analysis
CountryInflation (%)Unemployment (%)
USA3.73.8
India5.57.2
Critical Evaluation
  • 2023 data shows r=-0.62, but omitted variables like supply shocks distort results.
  • During COVID, the Phillips Curve broke down despite high correlation historically.
Future Implications

Economists now combine it with regression analysis for better predictions.

Question 8:
Compare time series and cross-sectional data in analyzing India's GDP growth (2018-2023).
Answer:
Theoretical Framework

Time series tracks variables over time, while cross-sectional compares units at one point. Both are vital for GDP analysis.

Evidence Analysis
  • Time series: India's quarterly GDP grew from 4.5% (2018) to 6.1% (2023).
  • Cross-section: In 2023, Maharashtra (8.2%) grew faster than Bihar (3.4%).
Critical Evaluation

While time series shows recovery post-COVID, cross-section reveals regional disparities.

Future Implications

Combining both helps design targeted policies like the PM Gati Shakti scheme.

Question 9:
Evaluate the effectiveness of index numbers in measuring inflation, citing WPI and CPI differences.
Answer:
Theoretical Framework

Index numbers like WPI (wholesale) and CPI (consumer) track price changes using base-year comparisons.

Evidence Analysis
  • 2023 CPI (6.7%) was higher than WPI (3.9%) due to food weightage differences.
  • WPI excludes services, underestimating education/healthcare inflation.
Critical Evaluation

While CPI better reflects household burdens, both fail to capture quality improvements like smartphones.

Future Implications

RBI now uses core inflation (excluding volatile items) for monetary policy.

Question 10:
Discuss how sampling methods affect the accuracy of unemployment surveys, with NSSO and CMIE examples.
Answer:
Theoretical Framework

Sampling methods (random, stratified) determine data reliability. Our textbook emphasizes representative samples.

Evidence Analysis
  • NSSO's stratified sampling (2022) showed 6.1% unemployment vs CMIE's 7.8% (convenience sampling).
  • CMIE overrepresents urban youth due to mobile-based data collection.
Critical Evaluation

While NSSO is methodologically robust, its 5-year lag misses real-time changes like post-COVID job losses.

Future Implications

Hybrid models using PANEL data are emerging for dynamic labor market analysis.

Question 11:
Explain the importance of measures of central tendency in economic data analysis with suitable examples. How do they help in simplifying complex data sets?
Answer:

In economics, measures of central tendency like mean, median, and mode are essential tools for summarizing large data sets into a single representative value. They help economists and policymakers make informed decisions by identifying trends and patterns.

Mean (average) is widely used to analyze data like per capita income or GDP growth rates. For example, calculating the mean income of a country helps compare economic performance over time.

Median (middle value) is useful when data has extreme values (outliers). For instance, median household income provides a better measure than mean income if wealth inequality is high.

Mode (most frequent value) helps identify common trends, such as the most demanded product price in a market.

These measures simplify complex data by:

  • Providing a quick snapshot of data distribution.
  • Enabling comparisons between different data sets.
  • Reducing large volumes of data into understandable figures.

Thus, measures of central tendency are fundamental in economic analysis for accurate and efficient decision-making.

Question 12:
Explain the measures of central tendency with suitable examples. How do they help in summarizing data effectively?
Answer:

The measures of central tendency are statistical tools used to identify the central or typical value in a dataset. The three main measures are:

  • Mean: The average of all values. For example, the mean of 5, 10, and 15 is (5 + 10 + 15)/3 = 10.
  • Median: The middle value when data is arranged in order. For the numbers 3, 7, 9, the median is 7.
  • Mode: The most frequently occurring value. In the dataset 2, 4, 4, 6, the mode is 4.

These measures help summarize data by providing a single representative value, making it easier to interpret large datasets. The mean is useful for continuous data, the median for skewed distributions, and the mode for categorical data. Together, they offer a comprehensive understanding of the dataset's central behavior.

Question 13:
Explain the measures of central tendency with suitable examples. How do they help in analyzing economic data?
Answer:

The measures of central tendency are statistical tools used to identify the central or typical value in a dataset. The three main measures are:

  • Mean: The average of all values. For example, if the incomes of 5 people are ₹10,000, ₹15,000, ₹20,000, ₹25,000, and ₹30,000, the mean income is (10,000 + 15,000 + 20,000 + 25,000 + 30,000) / 5 = ₹20,000.
  • Median: The middle value when data is arranged in order. In the above example, the median is ₹20,000.
  • Mode: The most frequently occurring value. If another person earns ₹15,000, the mode becomes ₹15,000.

These measures help economists analyze data by:

  • Providing a summary of large datasets.
  • Identifying trends, such as average income or consumption patterns.
  • Comparing different groups or time periods, like GDP growth across years.

For instance, policymakers use the mean to assess average household income, while businesses might use the mode to identify the most popular product price range. However, outliers can skew the mean, so median is often preferred for income distribution analysis.

Question 14:
Explain the importance of measures of central tendency in economic data analysis with suitable examples. How do they help in simplifying complex data sets? (5 marks)
Answer:

In economics, measures of central tendency like mean, median, and mode are essential tools for summarizing large datasets into a single representative value. They simplify complex economic data, making it easier to interpret trends and make informed decisions.

Mean (average) is widely used to analyze income levels, GDP growth, or inflation rates. For example, calculating the mean income of a country helps policymakers assess economic well-being.

Median is useful when data has extreme values (outliers), such as wealth distribution, where a few billionaires can skew the mean. Median income provides a clearer picture of what an average person earns.

Mode identifies the most frequent occurrence, like the most common price of a commodity in a market survey.

These measures help in:

  • Simplifying comparisons between different economic groups or time periods.
  • Identifying trends such as rising prices or falling employment rates.
  • Supporting decision-making for businesses and governments by providing clear benchmarks.

Thus, central tendency measures are foundational in transforming raw economic data into actionable insights.

Question 15:
Explain the measures of central tendency with suitable examples. How do they help in summarizing large datasets in economics?
Answer:

Measures of central tendency are statistical tools used to identify the center or average of a dataset. The three primary measures are:

  • Mean: The arithmetic average, calculated by summing all values and dividing by the number of observations.
    Example: If monthly incomes of 5 households are ₹10,000, ₹15,000, ₹20,000, ₹25,000, and ₹30,000, the mean income is (10,000 + 15,000 + 20,000 + 25,000 + 30,000) / 5 = ₹20,000.
  • Median: The middle value when data is arranged in ascending/descending order.
    Example: For the incomes above, the median is ₹20,000.
  • Mode: The most frequently occurring value.
    Example: If ages of students are 18, 18, 19, 20, 20, 20, the mode is 20.

These measures help economists summarize large datasets by providing a single representative value, simplifying comparisons, and identifying trends. For instance, mean income helps assess overall economic status, while median reduces the impact of extreme values (like outliers in income distribution).

Question 16:
Describe the steps involved in constructing a frequency distribution table from raw economic data. Why is it useful for statistical analysis?
Answer:

Constructing a frequency distribution table involves the following steps:

  1. Determine the range: Subtract the smallest value from the largest in the dataset.
    Example: If GDP growth rates range from 2% to 8%, the range is 8 - 2 = 6.
  2. Decide the number of classes: Typically, use 5-15 classes based on data size.
    For the GDP example, 5 classes (e.g., 2-3.2%, 3.2-4.4%, etc.) may be chosen.
  3. Calculate class width: Divide the range by the number of classes.
    Here, 6/5 = 1.2, so each class has a width of 1.2.
  4. List class intervals: Ensure no overlap (e.g., 2-3.2, 3.2-4.4).
  5. Tally and count frequencies: Record how many observations fall in each interval.

A frequency table is useful because it:

  • Simplifies raw data into manageable groups.
  • Highlights patterns (e.g., most GDP growth rates clustered around 4-6%).
  • Forms the basis for graphs like histograms, aiding visual analysis in economics.
Question 17:
Explain the importance of measures of central tendency in statistical analysis with suitable examples. How do they help in summarizing data effectively?
Answer:

Measures of central tendency are statistical tools that help in identifying the central or typical value in a dataset. They include the mean, median, and mode, each serving a unique purpose in data analysis.

Mean is the average of all data points and is useful for datasets without extreme values. For example, calculating the average income of a group gives a fair representation of their economic status.

Median is the middle value when data is arranged in order. It is less affected by outliers, making it ideal for skewed data. For instance, median household income provides a better measure than mean in areas with income inequality.

Mode represents the most frequently occurring value and is useful for categorical data, such as identifying the most common shoe size in a store.

These measures summarize large datasets into single values, making it easier to compare groups, identify trends, and make informed decisions. They are foundational in fields like economics, where understanding distributions of income, prices, or other variables is crucial.

Question 18:
Describe the process of constructing a histogram for a given frequency distribution. What are its advantages over a bar graph in representing continuous data?
Answer:

A histogram is a graphical representation of a frequency distribution for continuous data. Here’s how to construct one:

  • Step 1: Determine the range of the data (maximum value - minimum value).
  • Step 2: Decide the number of intervals (classes) and calculate the class width (range ÷ number of classes).
  • Step 3: Create class boundaries and tally the frequencies for each class.
  • Step 4: Draw the x-axis (class intervals) and y-axis (frequency).
  • Step 5: Plot rectangles for each class with heights proportional to their frequencies.

Advantages over a bar graph:

  • Histograms display continuous data seamlessly, with no gaps between bars (unless there’s a zero frequency), while bar graphs represent discrete categories with gaps.
  • They show the shape of the distribution (e.g., normal, skewed), helping identify patterns like central tendency and spread.
  • Histograms are better for large datasets, as they group data into intervals, making trends clearer.

For example, a histogram of monthly rainfall data clearly shows seasonal patterns, whereas a bar graph would treat each month as separate, losing the continuity.

Question 19:
Explain the measures of central tendency with suitable examples. How do they help in summarizing data effectively in economics?
Answer:

The measures of central tendency are statistical tools used to identify the center or average of a dataset. The three primary measures are:

  • Mean: The arithmetic average, calculated by summing all values and dividing by the number of observations. For example, if the incomes of five individuals are ₹10,000, ₹15,000, ₹20,000, ₹25,000, and ₹30,000, the mean income is (10,000 + 15,000 + 20,000 + 25,000 + 30,000) / 5 = ₹20,000.
  • Median: The middle value when data is arranged in ascending or descending order. In the above example, the median is ₹20,000. If there is an even number of observations, the median is the average of the two middle values.
  • Mode: The most frequently occurring value in a dataset. For example, if the ages of students in a class are 16, 17, 17, 18, and 19, the mode is 17.

These measures help economists summarize large datasets into a single representative value, making it easier to analyze trends, compare groups, and make informed decisions. For instance, the mean income helps assess overall economic well-being, while the median is less affected by extreme values, providing a clearer picture of typical income.

Question 20:
Describe the steps involved in constructing a frequency distribution table from raw data. Why is it useful in economic analysis?
Answer:

Constructing a frequency distribution table involves the following steps:

  1. Determine the range: Subtract the smallest value from the largest value in the dataset.
    Example: If the highest income is ₹50,000 and the lowest is ₹10,000, the range is ₹40,000.
  2. Decide the number of classes: Typically, 5 to 15 classes are used, depending on data size.
    For simplicity, let’s choose 5 classes.
  3. Calculate class width: Divide the range by the number of classes and round up.
    ₹40,000 / 5 = ₹8,000 per class.
  4. Define class intervals: Create non-overlapping intervals (e.g., ₹10,000–₹18,000, ₹18,001–₹26,000, etc.).
  5. Tally the frequencies: Count how many observations fall into each interval.
  6. Present the table: List classes alongside their frequencies.

A frequency distribution table is useful in economics as it organizes raw data into meaningful patterns, revealing trends like income inequality or consumer spending habits. It simplifies complex data, enabling policymakers to identify disparities and design targeted interventions.

Case-based Questions (4 Marks) – with Solutions (CBSE Pattern)

These 4-mark case-based questions assess analytical skills through real-life scenarios. Answers must be based on the case study provided.

Question 1:
A survey in Rural District X recorded monthly incomes (in ₹) of 50 farmers:
Income Range (₹)No. of Farmers
0-500012
5000-1000018
10000-1500015
15000+5
. Analyze central tendency and dispersion for policymaking.
Answer:
Case Deconstruction

The data shows income inequality, with 60% earning below ₹10,000. The median falls in the 5000-10000 range, indicating skewed distribution.

Theoretical Application
  • Mean would be inflated by the 15000+ group
  • Standard deviation would reveal high dispersion
Critical Evaluation

Policies like MSP hikes should target the 0-5000 group, as our textbook shows similar Lorenz curve patterns in agrarian economies.

Question 2:
The CPI for Industrial Workers (2023) shows:
ItemWeight (%)Price Rise (%)
Food469.2
Housing156.5
. Calculate weighted index and interpret inflation impact.
Answer:
Case Deconstruction

Food dominates the basket (46% weight) with 9.2% inflation, signaling severe pressure on low-income groups.

Theoretical Application
  • Weighted index = (46×9.2 + 15×6.5)/61 ≈ 8.3%
  • This exceeds RBI's 6% target, demanding monetary tightening
Critical Evaluation

As we studied, such inflation erodes purchasing power. Example: A ₹100 meal now costs ₹109.2, worse for daily-wage workers.

Question 3:
A scatter plot of GDP growth (%) vs FDI inflow ($bn) for 2015-20 shows r=0.78. Examine correlation and causality challenges.
Answer:
Case Deconstruction

Strong positive correlation (r=0.78) suggests FDI and GDP move together, like China's 2000s boom.

Theoretical Application
  • But spurious correlation may exist (both rising over time)
  • Need regression analysis to isolate FDI impact
Critical Evaluation

Our textbook warns against post hoc fallacy. Example: Service sector growth could independently boost both variables.

Question 4:
State A's literacy rate rose from 68% (2011) to 75% (2021), while per capita income grew from ₹55,000 to ₹89,000. Construct index numbers and assess development linkage.
Answer:
Case Deconstruction

Both indicators show progress, with income (61.8% rise) outpacing literacy (10.3% rise).

Theoretical Application
  • Literacy index: (75/68)×100 = 110.3
  • Income index: (89000/55000)×100 = 161.8
Critical Evaluation

This matches our study of human capital theory. Example: Kerala's high literacy enabled IT sector growth, but State A's gap suggests skill mismatch.

Question 5:
A time-series of Unemployment Rate (%) post-demonetization:
QuarterUR (%)
Q4 20164.9
Q1 20176.2
Q2 20177.5
. Identify trend and critique data limitations.
Answer:
Case Deconstruction

UR spiked by 2.6 percentage points in two quarters, confirming cyclical unemployment from cash crunch.

Theoretical Application
  • Missing informal sector data understates actual job losses
  • Need moving averages to smooth quarterly volatility
Critical Evaluation

As per PLFS reports, urban UR peaked at 8.4% (Q3 2017), showing our textbook's lag effect concept in policy shocks.

Question 6:
A survey recorded monthly incomes (in ₹) of 50 households in a village: Mean = 15,000, Median = 12,000, Mode = 10,000. Analyze the skewness and its economic implications.
Answer:
Case Deconstruction

The data shows Mean > Median > Mode, indicating positive skewness. This means higher-income households pull the average up.

Theoretical Application
  • Skewness reflects income inequality, as seen in our textbook’s Lorenz curve examples.
  • Policy focus should target redistribution (e.g., subsidies) to reduce disparity.
Critical Evaluation

Current data from NSSO (2022) shows similar skewness in rural India. Without intervention, poverty traps may worsen.

Question 7:
The correlation coefficient between education years and income is +0.78 for urban youth. Interpret this and suggest economic policies.
Answer:
Case Deconstruction

A +0.78 correlation implies a strong positive relationship, as we studied in scatter diagrams.

Theoretical Application
  • Invest in vocational training (e.g., PMKVY) to enhance skills-to-income linkage.
  • Subsidize higher education loans to reduce opportunity cost.
Critical Evaluation

ASER 2021 reports similar trends. Policies must address urban-rural education gaps for equitable growth.

Question 8:
A state’s GDP growth rate (2019-23) shows standard deviation of 2.5%. Discuss volatility and its impact on investment.
Answer:
Case Deconstruction

High standard deviation indicates unstable growth, deterring long-term capital formation.

Theoretical Application
  • Use fiscal buffers (e.g., Kerala’s resilience fund) to stabilize shocks.
  • Promote diversification (e.g., Tamil Nadu’s multi-sector approach).
Critical Evaluation

RBI’s 2023 report links volatility to investor hesitancy. Stable policies are critical.

Question 9:
Compare CPI and WPI trends (2020-23) using the table below. Explain divergence causes.
[Diagram: Table with CPI (5.1%, 6.7%, 5.8%) vs WPI (3.2%, 4.9%, 3.5%)]
Answer:
Case Deconstruction
YearCPIWPI
20205.1%3.2%
20216.7%4.9%
20225.8%3.5%
Theoretical Application
  • CPI includes services (e.g., healthcare), while WPI tracks goods (e.g., fuel).
  • 2021’s high CPI reflects supply-chain disruptions post-COVID.
Critical Evaluation

Our textbook highlights how food weightage (50% in CPI) drives divergence, as per NSO data.

Question 10:
A survey recorded the per capita income (in ₹) of five Indian states: Kerala (1,45,000), Punjab (1,30,000), Tamil Nadu (1,20,000), Bihar (45,000), and Uttar Pradesh (55,000). Analyze the data using statistical tools to compare economic disparities.
Answer:
Case Deconstruction

The data reveals stark income inequality, with Kerala’s per capita income being 3.2x Bihar’s. We studied how range (₹1,00,000) and mean (₹99,000) summarize disparities.

Theoretical Application
  • Standard deviation would quantify variability.
  • Bar diagrams can visually contrast state incomes.
Critical Evaluation

Our textbook shows such gaps require progressive taxation or targeted schemes like MGNREGA to reduce inequality.

Question 11:
A farmer recorded wheat yield (kg/acre) over 5 years: 2019 (520), 2020 (480), 2021 (510), 2022 (490), 2023 (530). Identify trends and suggest measures using time series analysis.
Answer:
Case Deconstruction

The yield fluctuates between 480-530 kg/acre, showing no consistent growth. We calculated the moving average (3-year: 503, 493, 510) to smooth variations.

Theoretical Application
  • Use linear regression to predict future yields.
  • 2020’s dip may reflect monsoon variability.
Critical Evaluation

Our textbook emphasizes irrigation investment and hybrid seeds to stabilize output, as seen in Punjab’s success.

Question 12:
The table shows CPI indices for urban (2022: 160, 2023: 168) and rural (2022: 155, 2023: 162) India. Interpret the inflation differential using statistical measures.
Answer:
Case Deconstruction

Urban CPI rose by 5% (168/160), while rural CPI increased by 4.5% (162/155). We studied how inflation rates diverge due to fuel price shocks.

Theoretical Application
  • Weighted average shows urban areas rely more on transport (15% weight vs. 8% rural).
  • 2023’s gap (6 points) widened from 2022 (5 points).
Critical Evaluation

Our textbook links this to MSP policies reducing rural inflation, as seen in Chhattisgarh’s PDS efficiency.

Question 13:
A study compares unemployment rates (%) among graduates: Delhi (12.5), Mumbai (10.8), Bengaluru (9.3), and Kolkata (14.2). Evaluate the regional imbalance using dispersion tools.
Answer:
Case Deconstruction

Kolkata’s rate is 1.5x Bengaluru’s, showing high variance. We calculated quartile deviation (Q3-Q1=2.45) to measure spread.

Theoretical Application
  • Coefficient of variation (18.7%) confirms uneven distribution.
  • Mumbai’s IT sector may explain lower rates.
Critical Evaluation

Our textbook cites skill mismatch as a key cause, similar to Tamil Nadu’s Naan Mudhalvan scheme addressing this gap.

Question 14:

A small business owner recorded the monthly sales (in ₹) of his shop for the first six months of 2025 as follows: 25,000, 28,000, 30,000, 32,000, 35,000, 40,000. The owner wants to analyze the trend in sales.

(a) Identify the statistical tool most suitable for this analysis.

(b) Calculate the average monthly sales for this period.

Answer:

(a) The most suitable statistical tool for analyzing the trend in sales is the arithmetic mean (average) as it provides a central value of the data set, helping to understand the overall performance.


(b) To calculate the average monthly sales, we use the formula:


Average = (Sum of all monthly sales) / (Number of months)
Sum of sales = 25,000 + 28,000 + 30,000 + 32,000 + 35,000 + 40,000 = ₹1,90,000
Number of months = 6
Average = 1,90,000 / 6 = ₹31,666.67 (approx)

Thus, the average monthly sales for the first six months of 2025 is approximately ₹31,666.67.

Question 15:

A researcher collected data on the monthly income (in ₹) of 10 families in a village: 12,000, 15,000, 18,000, 20,000, 22,000, 25,000, 28,000, 30,000, 35,000, 40,000.

(a) Identify the measure of central tendency that best represents this data and justify your choice.

(b) Calculate the chosen measure.

Answer:

(a) The measure of central tendency that best represents this data is the median. Since the data has a wide range (₹12,000 to ₹40,000) and potential outliers, the median is less affected by extreme values compared to the mean, providing a more accurate central value.


(b) To calculate the median:


Step 1: Arrange the data in ascending order (already given).
Step 2: Since there are 10 observations (even number), the median is the average of the 5th and 6th values.
5th value = ₹22,000
6th value = ₹25,000
Median = (22,000 + 25,000) / 2 = ₹23,500

Thus, the median monthly income of the families is ₹23,500.

Question 16:

A small-scale farmer recorded the monthly production of wheat (in quintals) for the past year as follows: 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38, 40. The farmer wants to analyze the data using measures of central tendency.

(a) Calculate the mean, median, and mode of the given data.

(b) Which measure would best represent the farmer's typical monthly production? Justify your answer.

Answer:

(a) Mean: Sum of all values divided by the number of observations.
Mean = (12 + 15 + 18 + 20 + 22 + 25 + 28 + 30 + 32 + 35 + 38 + 40) / 12
Mean = 315 / 12 = 26.25 quintals.

Median: Middle value when data is arranged in ascending order.
Since there are 12 observations (even), median = average of 6th and 7th values.
Median = (25 + 28) / 2 = 26.5 quintals.

Mode: Most frequently occurring value.
Here, no value repeats, so the data has no mode.

(b) The median (26.5 quintals) best represents the typical monthly production because:

  • The data has no extreme outliers, and the median is less affected by minor fluctuations.
  • It lies close to the mean, confirming its reliability as a central measure.

Question 17:

A school conducted a survey on the daily screen time (in hours) of 50 students and presented the data in a frequency distribution table:

Screen Time (hours)Number of Students
0-25
2-412
4-618
6-810
8-105

(a) Calculate the mean screen time using the assumed mean method (take A = 5).

(b) Interpret the result in the context of student health.

Answer:

(a) Assumed Mean Method:
Assumed mean (A) = 5, class width (h) = 2.
Calculations:

Class IntervalMidpoint (xi)Frequency (fi)di = (xi - A)/hfidi
0-215-2-10
2-4312-1-12
4-651800
6-8710110
8-1095210

Σfidi = -10 - 12 + 0 + 10 + 10 = -2
Σfi = 50
Mean = A + (Σfidi/Σfi) × h = 5 + (-2/50) × 2 = 5 - 0.08 = 4.92 hours.

(b) Interpretation:

  • The average screen time of 4.92 hours indicates moderate usage, but prolonged exposure may affect physical health (e.g., eye strain) and mental well-being.
  • Schools should promote balanced screen time to ensure students engage in offline activities.

Question 18:

A small-scale farmer in rural India recorded the monthly yield (in kg) of his wheat crop for 6 months as follows: 120, 135, 110, 150, 130, 125. He wants to analyze the central tendency of his yield data to plan better for the next season. Help him by:

  • Calculating the mean, median, and mode of the given data.
  • Explaining which measure of central tendency would be most useful for his analysis and why.
Answer:

Step 1: Calculate Mean
Mean = (Sum of all observations) / (Number of observations)
= (120 + 135 + 110 + 150 + 130 + 125) / 6
= 770 / 6
= 128.33 kg (approx)

Step 2: Calculate Median
First, arrange data in ascending order: 110, 120, 125, 130, 135, 150
Since there are 6 observations (even number), median is the average of 3rd and 4th values.
Median = (125 + 130) / 2 = 127.5 kg

Step 3: Calculate Mode
Since all values occur only once, there is no mode for this dataset.

Most Useful Measure: The median (127.5 kg) would be most useful because:

  • It is not affected by extreme values (like 150 kg).
  • Represents the middle value, giving a realistic estimate of typical yield.
  • More reliable for small datasets with potential fluctuations.
Question 19:

A school conducted a survey on the monthly pocket money (in ₹) received by 10 students of Class 11: 500, 600, 700, 500, 800, 1000, 500, 600, 700, 1200. The principal wants to understand the dispersion of this data to assess economic diversity.

  • Calculate the range and standard deviation (assume sample data).
  • Interpret the results in the context of the survey.
Answer:

Step 1: Calculate Range
Range = Maximum value - Minimum value
= 1200 - 500 = ₹700

Step 2: Calculate Standard Deviation
1. Mean (µ) = (500+600+700+500+800+1000+500+600+700+1200)/10 = 710
2. Calculate squared deviations:
(500-710)² = 44100, (600-710)² = 12100, (700-710)² = 100, etc.
3. Sum of squared deviations = 44100+12100+100+44100+8100+84100+44100+12100+100+240100 = 494,900
4. Variance = 494,900 / (10-1) = 54,988.89
5. Standard Deviation = √54,988.89 ≈ ₹234.50

Interpretation:

  • The range (₹700) shows a wide gap between minimum and maximum pocket money.
  • Standard deviation (₹234.50) indicates high variability in amounts received by students.
  • This suggests significant economic inequality among students, which may require attention for equitable policies.
Question 20:
A survey was conducted in a village to study the monthly income (in ₹) of 50 families. The data collected is as follows:
5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, 20000, 21000, 22000, 23000, 24000, 25000, 26000, 27000, 28000, 29000, 30000, 31000, 32000, 33000, 34000, 35000, 36000, 37000, 38000, 39000, 40000, 41000, 42000, 43000, 44000, 45000, 46000, 47000, 48000, 49000, 50000, 51000, 52000, 53000, 54000.
(a) Organize the data into a frequency distribution table with class intervals of ₹5000.
(b) Calculate the arithmetic mean of the monthly income.
Answer:

(a) Frequency Distribution Table:

Class Interval (₹)Frequency
5000-100005
10000-150005
15000-200005
20000-250005
25000-300005
30000-350005
35000-400005
40000-450005
45000-500005
50000-550005

(b) Arithmetic Mean Calculation:
Sum of all incomes = ₹1,475,000
Number of families = 50
Arithmetic Mean = Sum of incomes / Number of families = ₹1,475,000 / 50 = ₹29,500
Note: The mean represents the average income, providing a central value for the data set.

Question 21:
The following table shows the marks obtained by 30 students in an Economics test (out of 50):
MarksNumber of Students
10-204
20-306
30-4010
40-5010

(a) Draw a histogram to represent this data.
(b) Identify the modal class and justify your answer.
Answer:

(a) Histogram:
Note: Since a diagram cannot be drawn here, the steps to construct it are:
1. Label the x-axis as 'Marks' and the y-axis as 'Number of Students'.
2. Use equal-width bars for each class interval (10-20, 20-30, etc.).
3. The height of each bar corresponds to the frequency (number of students).
4. Ensure no gaps between bars as data is continuous.

(b) Modal Class: The modal class is 30-40 and 40-50 (both have the highest frequency of 10 students).
Justification: The modal class is the class interval with the highest frequency in a frequency distribution. Here, two classes share the highest frequency, making them both modal classes.

Question 22:
A researcher collected data on the monthly income (in ₹) of 10 families in a village: 15,000, 18,000, 22,000, 12,000, 25,000, 30,000, 20,000, 17,000, 19,000, 28,000. The village head claims that the average income is ₹20,000. Using statistical tools, verify this claim and explain your steps.
Answer:

To verify the village head's claim, we calculate the arithmetic mean (average income) of the given data.


Step 1: Sum all incomes
15,000 + 18,000 + 22,000 + 12,000 + 25,000 + 30,000 + 20,000 + 17,000 + 19,000 + 28,000 = ₹2,06,000

Step 2: Divide by number of families (n=10)
Mean = Total Income / n = 2,06,000 / 10 = ₹20,600

The calculated mean (₹20,600) is slightly higher than the claimed ₹20,000. The difference may arise due to rounding or sample selection. However, the claim is approximately correct as the values are close.

Question 23:
The following table shows the marks (out of 100) of 8 students in Economics and Mathematics:
StudentEconomicsMathematics
A7580
B8278
C6872
D9085
E5560
F7882
G8588
H7275

Calculate the range for both subjects and interpret the results. Which subject has greater variability in marks?
Answer:

Range is calculated as the difference between the highest and lowest values in a dataset.


Step 1: Economics Marks
Highest = 90, Lowest = 55
Range = 90 - 55 = 35

Step 2: Mathematics Marks
Highest = 88, Lowest = 60
Range = 88 - 60 = 28

Interpretation: The range for Economics (35) is higher than Mathematics (28), indicating greater variability in Economics marks. This suggests that students' performance in Economics varies more widely compared to Mathematics.

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