Chapter 4, Problem 2PP

Mean and standard deviation. Write a program that reads a set of floating-point data values. Choose an appropriate mechanism for prompting for the end of the data set. When all values have been read, print out the count of the values, the average, and the standard deviation. The average of a data set $\left\{x_1,\mathrm{....},x_n\right\}$ is $\bar{x}={\displaystyle \sum x_i}/n$, where ${\displaystyle \sum x_i}=x_1+\mathrm{...}+x_n$ is the sum of the input values. The standard deviation is

$s=\sqrt{\frac{\Sigma {\left(x_i-\bar{x}\right)}^2}{n-1}}$

However, this formula is not suitable for the task. By the time the program has computed $\bar{x}$, the individual x_i are long gone. Until you know how to save these values, use the numerically less stable formula

$s=\sqrt{\frac{\sum x_i^2-\frac{1}{n}{\left(\sum x_i\right)}^2}{n-1}}$

You can compute this quantity by keeping track of the count, the sum, and the sum of squares as you process the input values.