Question

The mean of 200 items is 48 and standard deviation is 3 . The sum of square of all the items is?

Answer 1

Answer:

The sum of square of all the items is 4104.

Step-by-step explanation:

The formula of standard deviation is:

$SD=\sqrt{\frac{1}{N}[\sum X^{2}-\mu^{2}]}$

Given:

N = 200

SD = 3

μ = 48

Compute the value of ∑ X² as follows:

$SD=\sqrt{\frac{1}{N}[\sum X^{2}-\mu^{2}]}\\3=\sqrt{\frac{1}{200}[\sum X^{2}-48^{2}]}\\9=\frac{1}{200}[\sum X^{2}-2304]\\1800=\sum X^{2}-2304\\\sum X^{2}=2304+1800\\\sum X^{2}=4104$

Thus, the sum of square of all the items is 4104.