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Economics · Class 11 Commerce

Ch 17Correlation — Class 11 Economics, concept-first.

In earlier chapters you learnt how to build summary measures — averages and measures of dispersion — out of a mass of data on a single variable. This chapter turns to a different question: how do we examine the relationship between two variables? Many pairs of variables in economics and everyday life seem to move toget…

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Key concepts

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Pearson Correlation

Imagine you're tracking two things over time — say, the number of ice creams sold at your school canteen and the outside temperature. On hot days, both go up; on cool days, both drop. They seem to move together.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

6.1

Introduction

In earlier chapters you learnt how to build summary measures — averages and measures of dispersion — out of a mass of data on a single variable.

6.2

Types Of Relationship

Relationships between two variables come in different forms, and it is worth classifying them before measuring anything.

6.2.1

What Does Correlation Measure?

Correlation studies and measures the direction and the intensity of the relationship among variables. It tells us both which way two variables move relative to each other and how closely they move tog…

6.2.2

Types Of Correlation

Correlation is commonly classified into two kinds according to the direction in which the variables move.

6.3

Techniques For Measuring Correlation

Three important tools are used to study the correlation between two variables:

6.3.1

Scatter Diagram

A scatter diagram is a simple visual technique for examining the form of a relationship without computing any number.

6.3.2

Karl Pearson's Coefficient Of Correlation

Karl Pearson's coefficient of correlation — also called the product moment or simple correlation coefficient — gives a precise numerical value for the degree of linear relationship between two variabl…

6.3.3

Properties Of Correlation Coefficient

The correlation coefficient has several important properties.

6.3.4

Step Deviation Method To Calculate Correlation Coefficient

When the values of the variables are large, computing directly is tedious. The step deviation method cuts the labour by exploiting the property that is independent of change of origin and scale.

6.3.5

Spearman's Rank Correlation

Spearman's rank correlation, developed by the British psychologist C. E. Spearman, measures the linear association between the ranks assigned to items rather than their actual values.

6.3.6

Calculation Of Rank Correlation Coefficient

The rank correlation coefficient is computed under three situations: (1) the ranks are already given, (2) the ranks must be worked out from the data, and (3) some ranks are repeated.

6.4

Conclusion

This chapter set out techniques for studying the relationship between two variables, especially a linear relationship.

Recap

- Correlation analysis studies the relationship between two variables. - A scatter diagram gives a visual presentation of the nature of that relationship.

Worked Examples

Solved examples, worked out step by step.

+Show 5 questions5 questions
  1. Example 1**Example 1.** Calculate the Karl Pearson's coefficient of correlation between the number of years of schooling of farmers and the annual yi…Free
  2. Example 2**Example 2.** Using the step deviation method, calculate the coefficient of correlation between price index (X) and money supply (Y). | Pri…Free
  3. Example 3**Example 3.** Five persons are assessed by three judges in a beauty contest. We have to find out which pair of judges has the nearest appro…Preview
  4. Example 4**Example 4.** We are given the percentage of marks secured by 5 students in Economics and Statistics. Work out the rankings and calculate t…Preview
  5. Example 5**Example 5.** The values of X and Y are given as follows. Work out the ranks (giving common ranks to repeated items) and calculate the Spea…Preview

Exercises

+Show 20 questions20 questions
  1. Q1The unit of correlation coefficient between height in feet and weight in kgs is (i) kg/feet (ii) percentage (iii) non-existentFree
  2. Q2The range of simple correlation coefficient is (i) 0 to infinity (ii) minus one to plus one (iii) minus infinity to infinityFree
  3. Q3If r xy is positive the relation between X and Y is of the type (i) When Y increases X increases (ii) When Y decreases X increases (iii) Whe…Free
  4. Q4If r xy = 0 the variable X and Y are (i) linearly related (ii) not linearly related (iii) independentPreview
  5. Q5Of the following three measures which can measure any type of relationship (i) Karl Pearson's coefficient of correlation (ii) Spearman's ran…Preview
  6. Q6If precisely measured data are available the simple correlation coefficient is (i) more accurate than rank correlation coefficient (ii) less…Preview
  7. Q7Why is r preferred to covariance as a measure of association?Preview
  8. Q8Can r lie outside the –1 and 1 range depending on the type of data?Preview
  9. Q9Does correlation imply causation?Preview
  10. Q10When is rank correlation more precise than simple correlation coefficient?Preview
  11. Q11Does zero correlation mean independence?Preview
  12. Q12Can simple correlation coefficient measure any type of relationship?Preview
  13. Q13Collect the price of five vegetables from your local market every day for a week. Calculate their correlation coefficients. Interpret the re…Preview
  14. Q14Measure the height of your classmates. Ask them the height of their benchmate. Calculate the correlation coefficient of these two variables.…Preview
  15. Q15List some variables where accurate measurement is difficult.Preview
  16. Q16Interpret the values of r as 1, –1 and 0.Preview
  17. Q17Why does rank correlation coefficient differ from Pearsonian correlation coefficient?Preview
  18. Q18Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y). | X | 65 | 66 | 57 | 67 | 68 | 69 | 7…Preview
  19. Q19Calculate the correlation coefficient between X and Y and comment on their relationship: | X | –3 | –2 | –1 | 1 | 2 | 3 | |---|---|---|---|-…Preview
  20. Q20Calculate the correlation coefficient between X and Y and comment on their relationship: | X | 1 | 3 | 4 | 5 | 7 | 8 | |---|---|---|---|---|…Preview