Question

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is​

Answer 1

Answer:

The answer is 120 yes i think it is right

Answer 2

Answer:

160900

Step-by-step explanation:

Given:

Mean, $\bar{x}=40$

Number of observations, $n=100$

Standard deviation, $\sigma =3$

To find: Sum of squares of all deviations, $\sum x_{i}^{2}=?$

Variance is given as the square of standard deviation.

So, variance = $\sigma^{2}=3^{2}=9$

Now, we know that,

Variance is given as,

$\sigma^{2}=\frac{\sum x_{i}^{2}}{n}-(\bar x)^{2}\\\\9=\frac{\sum x_{i}^{2}}{100}-(40)^{2}\\\\9=\frac{\sum x_{i}^{2}}{100}-1600\\\\\frac{\sum x_{i}^{2}}{100}=9+1600\\\\\frac{\sum x_{i}^{2}}{100}=1609\\\\\sum x_{i}^{2}=1609\times 100=160900$

Therefore, the sum of squares of all deviations is​ 160900.