mathematics>Statistics>Correlation Analysis>Karl Pearson's Correlation Coefficient

Karl Pearson's Correlation Coefficient

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Karl Pearson's Correlation Coefficient: Overview

This Topic covers sub-topics such as Co-variance, Karl Pearson's Coefficient of Correlation, Spurious Correlation, Limitations of Correlation and, Interpretation of Karl Pearson's Coefficient

Important Questions on Karl Pearson's Correlation Coefficient

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 1

Find the Karl Pearson’s correlation coefficient between the marks in statistics and mathematics of 6 students. (out of 10)

$\begin{array}{lcccccc} Student & 1 & 2 & 3 & 4 & 5 & 6 \\ Statistics & 7 & 4 & 6 & 9 & 3 & 8 \\ Mathematics & 8 & 5 & 4 & 8 & 3 & 6 \end{array}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 2

Find the Karl Pearson’s coefficient of correlation for the following data:

$\begin{matrix} x & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ y & 15 & 16 & 14 & 13 & 11 & 12 & 10 & 8 & 9 \end{matrix}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 3

Find the correlation coefficient $r$ for the given data : $cov (X, Y) = 18 .6$ , variance of $X = 20.2$ , variance of $Y = 23.7$ .

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 4

State the limitations of correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$21$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 5

State the limitations of correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$20$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 6

State the limitations of correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$19$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 7

State the limitations of correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$18$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 8

State the limitations of correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$17$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 9

What is spurious correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$16$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 10

What is spurious correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$15$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 11

What is spurious correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$14$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 12

What is spurious correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

Marks in test $- 1$	$13$	$9$	$8$	$10$	$11$	$13$	$7$
Marks in test $- 2$	$14$	$8$	$6$	$9$	$11$	$12$	$3$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 13

What is spurious correlation. The following are the marks scored by $7$ students in two tests in a subject. Calculate the coefficient of correlation from the following data and interpret.

$\begin{array}{ll} Marks in test -1 & 12 & 9 & 8 & 10 & 11 & 13 & 7 \\ Marks in test -2 & 14 & 8 & 6 & 9 & 11 & 12 & 3 \end{array}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 14

Compute Karl Pearson's Coefficient of Correlation between sales and expenditures of a firm for six months.

Sales (in lakh of ₹)	$18$	$20$	$27$	$20$	$21$	$29$
Expenditure (in lakh of ₹)	$23$	$27$	$28$	$28$	$29$	$30$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 15

Calculate the coefficient of correlation between $X$ and $Y$ from the following data using Karl Pearson's method for the following data.

$x$	$2$	$5$	$3$	$4$	$6$
$y$	$3$	$8$	$6$	$4$	$9$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 16

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to three decimal values)

$\begin{matrix} x & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ y & 15 & 16 & 14 & 13 & 11 & 12 & 10 & 8 & 10 \end{matrix}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 17

Given that $cov (X, Y) = 20$ , variance of $X = 22$ , variance of $Y = 24$ . Find $r$ .(Answer up to three decimal places).

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 18

Calculate the Karl Pearson’s correlation coefficient between the marks (out of $10$ ) in science and biology of $6$ students.(Answer up to three decimal places)

$\begin{array}{lcccccc} Student & 1 & 2 & 3 & 4 & 5 & 6 \\ science & 8 & 4 & 6 & 9 & 3 & 8 \\ Biology & 8 & 5 & 4 & 8 & 3 & 6 \end{array}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 19

Calculate the Karl Pearson’s correlation coefficient between the marks in statistics and mathematics of $6$ students.(Answer up to three decimal places).

$\begin{array}{lcccccc} Student & 1 & 2 & 3 & 4 & 5 & 6 \\ Statistics & 7 & 4 & 6 & 9 & 3 & 8 \\ Mathematics & 8 & 5 & 4 & 8 & 3 & 6 \end{array}$

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mathematics>Correlation Analysis>Karl Pearson's Correlation Coefficient> Q 20

Calculate the Karl Pearson’s coefficient of correlation for the following data and interpret.(Answer up to two decimal values)

$\begin{matrix} x & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ y & 15 & 16 & 14 & 13 & 11 & 12 & 10 & 8 & 9 \end{matrix}$