Question

Calculate the number of items,when standard deviation of series X is 6 and coefficient of correlation is 0.75.Also given that sum of the product of deviations of X and Y from actual mean is 180 and sum of squares of deviation of Y from actual mean is 160​

Answer 1

Answer:

r= {xy/√{x²×{y²

0.75=180/√{x²×160

(0.75²)=(180²)/{x²×160

0.5625=32,400/{x²×160

x²=32,400/160×0.5625=32,400/90=360

{x²=360

standard deviation=√{x²/N

6=√360/N

(6²)=360/N

N=360/36=10

NUMBER OF ITEMS = 10

Answer 2

Given:

standard deviation of series= 6

The coefficient of correlation is equal to 0.75

To Find:

No of items

Explanation:

For the number of items we will use formula

r= xy / (x² × y²)

0.75=180/√(x²×160)

(0.75)²=(180)²÷(x²×160)

0.5625=32,400÷(x²×160)

x² = 32400÷160×0.5625

    = (32400 ÷90) = 360

x² = 360

For standard deviation=√(x²÷N)

6=√360 ÷N

(6²)=360÷N

N=360÷36=10

NUMBER OF ITEMS = 10

The Answer is 10