Chapter 12, Problem 15SGR

To determine

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

Answer to Problem 15SGR

The mean, variance and standard deviation of the data is $\text{18}\text{.2}$ , $40.16$ and $6.33$ .

Explanation of Solution

Given information:

The data is : $10,11,11,10,12,13,14,10$

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

  $\begin{array}{l}\text{mean}=\frac{10+11+11+10+12+13+14+10}{8}\\ \text{mean}=\frac{91}{8}\text{ [add]}\\ \text{mean=18}\text{.2 [divide]}\end{array}$

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,

  $\begin{array}{l}\text{variance}=\frac{67.24+51.84+51.84+67.24+38.44+27.04+17.64+67.24}{8}\text{ [subtract and square]}\\ \text{variance}=\frac{321.28}{8}\text{ [add]}\\ \text{variance}=40.16\text{ [divide]}\end{array}$

To find the standard deviation, square root the variance,

  $\begin{array}{l}\text{standard deviation}=\sqrt{40.16}\\ \text{standard deviation}=6.33\end{array}$