Chapter 5, Problem 5.45PE

(Statistics: compute mean and standard deviation) In business applications, you are often asked to compute the mean and standard deviation of data. The mean is simply the average of the numbers. The standard deviation is a statistic that tells you how tightly all the various data are clustered around the mean in a set of data. For example, what is the average age of the students in a class? How close are the ages? If all the students are the same age, the deviation is 0.

Write a program that prompts the user to enter 10 numbers and displays the mean and standard deviations of these numbers using the following formula:

     $\begin{array}{cc}\text{mean}=\frac{{\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i}}{n}=\frac{x_1+x_2+\cdots +x_n}{n}& \text{deviation}\text{=}\sqrt{\frac{{\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i^2}-\frac{{\left({\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i}\right)}^2}{n}}{n-1}}\end{array}$

Here is a sample run:

Enter 10 numbers: 1 2 3 4.5 5.6 6 7 8 9 10

The mean is 5 .61

The standard deviation is 2.99794