Question

The mean of 25 observations is N,the total of the observations is 300,while the total sum is 625,find N,and the standard deviation of the observation

Answer 1

The sample mean

$$N={\displaystyle\sum_{i=1}^nx_i \over n}$$

Given that $\displaystyle\sum_{i=1}^nx_i=300, n=25.$ Then

$$N={300\over 25}=12$$

The standard deviation of the observation

$$\sigma=\sqrt{{\displaystyle\sum_{i=1}^n(x_i-N)^2 \over n}}$$

Given that $\displaystyle\sum_{i=1}^n(x_i-N)^2=625.$ Then

$$\sigma=\sqrt{{625 \over 25}}=5$$

The mean of 25 observations is $N=12.$

The standard deviation of the observation is $\sigma=5.$