SUMMARY: This chapter focuses on the application of statistical tools in analyzing economic data and understanding economic phenomena.
KEY TOPICS: measures of central tendency, measures of dispersion, correlation, index numbers, time series analysis, graphical representation of data, frequency distribution, sampling methods, data interpretation, statistical inference
The Human Development Index is an example of a:
The most appropriate statistical tool to study the inter-dependence between two variables is:
When income distribution is studied graphically, the best tool is:
The deflator used to convert nominal GDP into real GDP is a type of:
To analyse seasonal fluctuations in agricultural prices, the suitable tool is:
Which measure of central tendency is most affected by extreme values in a data set?
If the mean of 5 observations is 10 and one observation of value 10 is removed, what is the new mean?
Which of the following is NOT a measure of dispersion?
The coefficient of correlation always lies between:
A Laspeyre's Price Index uses which year's quantities as weights?
In a frequency distribution, the class with the highest frequency is called the:
If Karl Pearson's coefficient of correlation between two variables X and Y is -0.9, it indicates:
Which graphical method is most appropriate for representing the trend in a time series of national income over 10 years?
In stratified random sampling, the population is divided into groups called:
The standard deviation of a data set is 6 and its mean is 30. The coefficient of variation (CV) is:
State any two ways statistical tools are used in economic analysis.
How is CPI used to compute real income?
How can a Lorenz curve help in policy-making?
Why is correlation useful in economic analysis?
Outline the basic steps of a statistical project.
What is the arithmetic mean and how is it calculated for ungrouped data?
Define median and explain when it is preferred over the arithmetic mean.
What is a frequency distribution and why is it useful in statistical analysis?
Distinguish between range and standard deviation as measures of dispersion.
What is the coefficient of variation and what does it indicate?
Explain how statistical tools are applied in everyday economic analysis.
Describe how you would analyse monthly household expenditure data for a city using statistical tools.
Explain how CPI is used to convert nominal wages into real wages with a numerical example.
Outline the stages of conducting a small statistical project on unemployment in your locality.
Explain, with examples, how a combination of statistical tools can be used to study a key economic issue such as inflation.
Explain the concept of arithmetic mean as a measure of central tendency. Discuss its merits and demerits with suitable examples from economic data.
Assertion (A): Statistical tools are essential for evidence-based economic policy.
Reason (R): Quantitative evidence makes decisions more objective than reliance on opinion or anecdote.
Assertion (A): Correlation helps identify the relationship between economic variables.
Reason (R): It quantifies both the direction and the strength of the association between two variables.
Assertion (A): A statistical project is only as good as the data it uses.
Reason (R): Wrong or biased data produce conclusions that can mislead, no matter how sophisticated the analysis.
Assertion (A): Dividing nominal income by the CPI and multiplying by 100 gives real income.
Reason (R): This removes the effect of the general price level on the money value of income.
Assertion (A): Graphical methods are a useful complement to statistical analysis.
Reason (R): Diagrams often convey patterns and comparisons to the reader more quickly than tables.
Assertion (A): The arithmetic mean is affected by extreme values in a data set.
Reason (R): The arithmetic mean is calculated by summing all values and dividing by the number of observations, making it sensitive to outliers.
Assertion (A): Median is the best measure of central tendency for open-ended frequency distributions.
Reason (R): Median divides the distribution into two equal halves and does not require the actual values of extreme items for its calculation.
Assertion (A): Standard deviation is an absolute measure of dispersion.
Reason (R): Coefficient of variation is used to compare variability between two series with different units or means.
Statement 1: Statistical tools are used throughout economic research.
Statement 2: The choice of tool depends on the nature of the data and the question being asked.
Statement 1: The NSO releases key Indian economic data.
Statement 2: The RBI supplements this with financial and monetary statistics.
Statement 1: Sampling techniques are useful when the population is very large.
Statement 2: Every statistical enquiry in India is based on a full census of the population.
Statement 1: Data interpretation is as important as data collection.
Statement 2: The reliability of conclusions depends on the accurate interpretation of the numbers.
Statement 1: Dividing nominal income by CPI and multiplying by 100 yields real income.
Statement 2: This adjustment removes the influence of changes in the general price level.
Statement 1: The arithmetic mean is affected by extreme values in a data set.
Statement 2: The median is also affected by extreme values in a data set.
Statement 1: Standard deviation is the square root of variance.
Statement 2: A higher standard deviation indicates less dispersion in the data.
Statement 1: A correlation coefficient of +1 indicates a perfect positive correlation between two variables.
Statement 2: A correlation coefficient of 0 indicates a perfect negative correlation between two variables.
Study the statistical tool and typical application mapping:
| Tool | Typical economic application |
|---|---|
| Arithmetic mean | Average household income |
| Standard deviation / CV | Inequality across regions |
| Lorenz curve | Income / wealth inequality |
| Correlation | Relationship between income and consumption |
| CPI / WPI | Tracking inflation |
Study the poverty-line data and answer:
| Year | Rural poverty % | Urban poverty % | All India % |
|---|---|---|---|
| 1993-94 | 50.1 | 31.8 | 45.3 |
| 2004-05 | 41.8 | 25.7 | 37.2 |
| 2011-12 | 25.7 | 13.7 | 21.9 |
Study the following frequency distribution data and answer the questions below:
| Class Interval | Frequency (f) |
|---|---|
| 0 - 10 | 5 |
| 10 - 20 | 10 |
| 20 - 30 | 20 |
| 30 - 40 | 9 |
| 40 - 50 | 6 |
Study the following data on runs scored by two batsmen and answer the questions below:
| Batsman | Mean Runs | Standard Deviation |
|---|---|---|
| Batsman A | 50 | 10 |
| Batsman B | 50 | 5 |
Study the poverty-ratio trend and answer:
Based on the given diagram, answer the following:
Based on the given chart showing the frequency distribution of marks obtained by 50 students, answer the following:
Based on the given scatter diagram showing the relationship between study hours and marks obtained by students, answer the following:
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