Chapter 12.2, Problem 48S

To determine

To find: Mean, median, and mode to the nearest tenth fir the set of data.

Answer to Problem 48S

Mean of the data is 85.5, median of the data is 90 and mode of the data are 90 and 92.

Explanation of Solution

Given information:

The given set of data is 90, 85, 92, 99, 78, 82, 92, 90.

Calculation:

Arrange the data from least to greatest:

78, 82, 85, 90, 90, 92, 92, 99.

Since, mean is defined as the sum of the data divided by total number of data in a data set. Therefore,

  $\begin{array}{l}\text{mean}=\frac{78+82+85+90+90+92+92+99}{8}\\ \text{mean}=\frac{708}{8}\\ \text{mean}=85.5\end{array}$

Also, median of the data is middle number of the ordered data or the mean of the middle two numbers. Therefore,

  $\begin{array}{l}\text{Median}=\frac{90+90}{2}\\ \text{Median}=\frac{180}{2}\\ \text{Median}=90\end{array}$

And, mode of the data defined as the data that occurs most often. Therefore,

  $\text{Mode}=90,92$

Hence,

Mean of the data is 85.5, median of the data is 90 and mode of the data are 90 and 92.