Chapter 12.3, Problem 1P

To determine

To find: The mean, median, and mode of the given data set.

Answer to Problem 1P

  $\begin{array}{l}\text{Mean}=112.4\\ \text{Median}=109\\ \text{Mode}=\text{104}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$

Explanation of Solution

Given information:

A data set is given, bowling scores: $104,117,104,136,109,113,104$ .

Calculation:

Given data set is $104,117,104,136,109,113,104$ .

  $\begin{array}{l}\text{Mean}=\frac{\text{Sum of data values}}{\text{Total number of data values}}\\ \Rightarrow \text{Mean}=\frac{104+117+104+136+113+104}{7}\\ \Rightarrow \text{Mean}=112.4\end{array}$

Arranging data set in ascending order, $104,104,104,109,113,117,136$ .

Since number of data values are $7$ , an odd number. So, median would be the middle data value.

  $\text{Median}=109$ .

Mode is the data item that occurs the most times. Here mode is $104$ .

Since in the given data there is no outlier data value. Therefore, mean would be best measure to describe the data set.

Hence, for the given data set −

  $\begin{array}{l}\text{Mean}=112.4\\ \text{Median}=109\\ \text{Mode}=\text{104}\\ \text{Mean is the best measure to describe the data set}\text{.}\end{array}$