Chapter 12, Problem 13STP

To determine

To find: the mean, variance and standard deviation to the nearest tenth for each set of data.

Answer to Problem 13STP

The standard deviation of the data is $3.43$ .

Explanation of Solution

Given information:

The data is : $14,11,9,6,10,16,15,13,9,12,19,10$

Calculation: To find the mean add all data and divide it by the number of data,

  $\begin{array}{l}\text{mean}=\frac{14+11+9+6+10+16+15+13+9+12+19+10}{12}\\ \text{mean}=\frac{144}{12}\text{ [add]}\\ \text{mean=12 [divide]}\end{array}$

To find the variance, subtract each data from the mean of data and then square it and add and then divide by the numbers of data,

  $\begin{array}{l}\text{variance}=\frac{4+1+9+36+4+16+9+1+9+0+49+4}{12}\text{ [subtract and square]}\\ \text{variance}=\frac{142}{12}\text{ [add]}\\ \text{variance}=11.83\text{ [divide]}\end{array}$

To find the standard deviation, square root the variance,

  $\begin{array}{l}\text{standard deviation}=\sqrt{11.83}\\ \text{standard deviation}=3.43\end{array}$