Chapter B.2, Problem 9E

To determine

To calculate: To solve the mean, median and mode of the data set.

Answer to Problem 9E

Mean is $8.5$

Median is $7,8$

Mode is $7$

Explanation of Solution

Given: Data set is $4,12,7,16,8,9,7,5$

Formula Used:

Mean is sum of observations divided by total number of observations

Median is the middlemost data point of the arranged data in ascending order. If number of data points is odd, median is middle most number, while if number of data points is even, median is two middle numbers

Mode is the data point which appears the most number of times

Calculation:

Data points is given as follows:

  $4,12,7,16,8,9,7,5$

Mean is calculated as follows:

  $\begin{array}{l}Mode=\frac{4+12+7+16+8+9+7+5}{8}\\ Mode=\frac{68}{8}\\ Mode=8.5\end{array}$

Median is calculated follows:

First arranging the data points in ascending order as follows:

  $4,5,7,7,8,9,12,16$

Number of data points is equal to $8$ , which is even

Thus, median is $7,8$

Mode is calculated as follows:

Data point which is appearing maximum number of times is $7$ , which is appearing for $2$ times and rest data points are appearing for only $1$ time

Thus, mode is $7$

Conclusion:

Hence, Mean is $8.5$

Median is $7,8$

Mode is $7$