Question

If the coefficient of correlation between two variables is zero, it does not mean that the

variables are unrelated”. Comment. Find Karl Pearson’s correlation coefficient between age

and playing habits of the following students:

Age (Years) 15 16 17 18 19 20

No. of Students 250 200 150 120 100 80

Regular Players 200 150 90 48 30 12

Also calculate the probable error and point out if coefficient of correlation is significant.​

Answer 1

Answer:

answer kha h bhai

Answer 2

Answer:

0.992

Step-by-step explanation:

Concept

• A linear correlation coefficient with a value range of -1 to +1 is defined as Karl Pearson's coefficient of correlation. High negative correlation shows a value of -1, whereas a strong positive correlation suggests a value of +1.

Given

Playing habits of students

Find

• Calculate the probable error and point out if the coefficient of correlation is significant

Solution

$r=\frac{\sum d_{X} d_{Y}-\frac{\left(\sum d_{X}\right) \times\left(\sum d_{Y}\right)}{N}}{\sqrt{\sum d_{X}^{2}-\frac{\left(\sum d_{X}\right)^{2}}{N}} \times \sqrt{\sum d_{Y}^{2}-\frac{\left(\sum d_{Y}\right)^{2}}{N}}}$

$\text { or, } r=\frac{-210-\frac{3 \times(60)}{6}}{\sqrt{19-\frac{(3)^{2}}{6}} \times \sqrt{3950-\frac{(60)^{2}}{6}}}=\frac{-240}{\sqrt{17.5} \times \sqrt{3350}}$

$\text { or, } r=\frac{-240}{4.18 \times 57.88}=\frac{-240}{241.94}=-0.992$

$\therefore r=-0.992$

the coefficient of correlation between age group and playing habits is 0.992

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