Solve the Following Question.(2 Marks)

Question 12 Marks

In the calculation of the correlation coefficient between the height and weight of a group of students of a college, one investigator took the measurements in inches and pounds while the other investigator took the measurements in cm. and kg. Will they get the same value of the correlation coefficient or different values? Justify your answer.

Answer

The coefficient of correlation is a ratio of covariance and standard deviations.
Since covariance and standard deviations are independent of units of measurement.
∴ coefficient of correlation is also independent of units of measurement.
∴ values of coefficient of correlation obtained by first and second investigators are the same.

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Question 22 Marks

Two series of x and y with 50 items each have standard deviations of 4.8 and 3.5 respectively. If the sum of products of deviations of x and y series from respective arithmetic means is 420, then find the correlation coefficient between x and y.

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Question 32 Marks

The correlation coefficient between x and y is 0.3 and their covariance is 12. The variance of x is 9, find the standard deviation of y.

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Question 42 Marks

The correlation coefficient between two variables x and y are 0.48. The covariance is 36 and the variance of x is 16. Find the standard deviation of y.

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Question 52 Marks

Find correlation coefficient between $\mathrm{x}$ andy series for the following data:
$
\mathrm{n}=15, \bar{x}=25, \bar{y}=18, \sigma_{\mathrm{x}}=3.01, \sigma_{\mathrm{y}}=3.03, \sum\left(x_{\mathrm{i}}-\bar{x}\right)\left(y_{\mathrm{i}}-\bar{y}\right)=122
$

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Maths (commerce) Solve the Following Question.(2 Marks)

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