Answer to Question #103778 in Statistics and Probability for Simon mwanthi

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 $\sigma=5.$