Chapter 12, Problem 12PT

To determine

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

Answer to Problem 12PT

The mean, variance and standard deviation is $\text{11}\text{.5}$ , $2.72$ and $1.64$ .

Explanation of Solution

Given information:

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

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

  $\begin{array}{l}\text{mean}=\frac{10+10+12+14}{4}\\ \text{mean}=\frac{46}{4}\text{ [add]}\\ \text{mean=11}\text{.5 [divide]}\end{array}$

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,

  $\begin{array}{l}\text{variance}=\frac{2.25+2.25+.25+6.25}{4}\text{ [subtract and square]}\\ \text{variance}=\frac{11}{4}\text{ [add]}\\ \text{variance}=2.72\text{ [divide]}\end{array}$

To find the standard deviation, square root the variance,

  $\begin{array}{l}\text{standard deviation}=\sqrt{2.72}\\ \text{standard deviation}=1.64\end{array}$