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Mathematics and Statistics · Class 11 Commerce

Ch 14Correlation — Class 11 Mathematics and Statistics, concept-first.

In earlier chapters we studied a single variable at a time — its average, its spread, its skewness. Very often, though, two variables move together: as the amount spent on advertising rises, sales tend to rise; as the price of a good rises, the quantity demanded tends to fall; as a student's study hours rise, marks ten…

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Key concepts

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Karl Pearson's Coefficient of Correlation

Pearson's (or the equivalent direct-method formula) is a unit-free number between and measuring the strength and direction of the linear relationship between two variables, independent of the units either is measured in.

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CA Foundation

1 concept · 8 appearances

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Chapter contents

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Meaning and Types of Correlation

In earlier chapters we studied a single variable at a time — its average, its spread, its skewness. Very often, though, two variables move together: as the amount spent on advertising rises, sales ten…

2

Scatter Diagram

The simplest way to see correlation is to plot the paired observations as points on a graph, with one variable on the horizontal () axis and the other on the vertical () axis.

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Karl Pearson's Coefficient of Correlation

A scatter diagram shows direction but not an exact strength. Karl Pearson's coefficient of correlation, denoted (or ), measures the degree of linear correlation between two variables by a single numbe…

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Spearman's Rank Correlation Coefficient

Sometimes the data are not exact measurements but ranks — the order in which judges place competitors, or the positions of students in two subjects.

Exercises

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  1. Q9Calculate Karl Pearson's coefficient of correlation for the data: | $x$ | 2 | 4 | 6 | 8 | 10 | |---|---|---|---|---|---| | $y$ | 5 | 7 | 9 |…Free
  2. Q10In a competition, two judges awarded the following marks to five candidates. Compute Spearman's rank correlation coefficient. | Candidate |…Free
  3. Q11Karl Pearson's coefficient of correlation always lies between: (a) $0$ and $1$ (b) $-1$ and $+1$ (c) $-1$ and $0$ (d) $-\infty$ and $+\infty…Preview
  4. Q12Distinguish between Karl Pearson's coefficient of correlation and Spearman's rank correlation coefficient, and state one situation in which…Preview

More questions

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  1. Example 1State, with a reason, the type of correlation (positive, negative or none) you would expect between each pair of variables: (i) the amount a…Free
  2. Example 2A scatter diagram of two variables shows points that lie very close to a straight line running from the upper-left to the lower-right of the…Free
  3. Example 3Compute Karl Pearson's coefficient of correlation for the following data: | $x$ | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | $y$ | 2 |…Free
  4. Example 4The heights (in cm) and weights (in kg) of 8 students are given. Find Karl Pearson's coefficient of correlation. | Height $x$ | 65 | 66 | 67…Preview
  5. Example 5For 5 weeks the price of a commodity (in \₹) and the quantity demanded (in units) were recorded. Compute Karl Pearson's coefficient of corre…Preview
  6. Example 6The coefficient of correlation between $x$ and $y$ is $0.8$. New variables are defined as $u = \dfrac{x - 10}{2}$ and $v = \dfrac{y - 5}{3}$…Preview
  7. Example 7Two judges ranked six paintings by first recording marks out of a hundred. Compute Spearman's rank correlation coefficient between the two j…Preview
  8. Example 8Compute Spearman's rank correlation coefficient for the following data, which contain repeated values. | $x$ | 68 | 64 | 75 | 50 | 64 | 80 |…Preview