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Question

If r=0.5,xy=120,x2=90,σy=8, then n=


A

100

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B

10

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C

15

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D

50

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Solution

The correct option is B

10


Explanation for the correct option :

Step 1: Equation using standard deviation :

From the question, we know that r=0.5,xy=120,x2=90,andσy=8

The formula for the standard deviation is given by:

σy=y2n

From this, we have

8=y2n

Squaring both sides,

64n=y2

Step 2: Determination of the value of n:

Now the formula for the coefficient of correlation r is given by:

r=xyx2y2

Substituting the given values we get,

0.5=12090×64n

Squaring both sides,

0.52=120290×64n0.25=144005760nn=144005760(0.25)n=144001440n=10

Hence ,option B is correct.


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