Chapter 12.2, Problem 47S

To determine

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

Answer to Problem 47S

Mean of the data is approximately 29.3, median of the data is 29 and there is no mode for the given set of data.

Explanation of Solution

Given information:

The given set of data is 12, 25, 14, 35, 42, 27, 31, 48.

Calculation:

Arrange the data from least to greatest:

12, 14, 25, 27, 31, 35, 42, 48.

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

  $\begin{array}{l}\text{mean}=\frac{12+14+25+27+31+35+42+48}{8}\\ \text{mean}=\frac{234}{8}\\ \text{mean}\approx 29.3\end{array}$

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

  $\begin{array}{l}\text{Median}=\frac{27+31}{2}\\ \text{Median}=\frac{58}{2}\\ \text{Median}=29\end{array}$

And, mode of the data defined as the data that occurs most often. Since, no data repeats in the given set. Therefore,

No mode.

Hence,

Mean of the data is approximately 29.3, median of the data is 29 and there is no mode for the given set of data.