Chapter 10, Problem 10SGR

To determine

To calculate mean, median and mode

Answer to Problem 10SGR

Mean is 43, median is 40.5, mode is 81

Explanation of Solution

Given information:

The dataset is,

10,81,66,15

Formula used:

Mean is,

  $\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Median is,

  $M=\frac{{(\frac{n}{2})}^{th}+{(\frac{n}{2}+1)}^{th}}{2}$

Mode is,

  $z=\max value$

Calculation:

For mean, substituting the values,

  $\overline{x}=\frac{10+81+66+15}{4}$

So,

  $\overline{x}=\frac{172}{4}$

On solving,

  $\overline{x}=43$

Hence, mean is 43.

Re-arranging the data in ascending order,

10,15,66,81

For median, substituting the value,

  $M=\frac{{(\frac{4}{2})}^{th}+{(\frac{4}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{2^{nd}+3^{rd}}{2}$

Substituting the values,

  $M=\frac{15+66}{2}$

On solving,

  $M=40.5$

Hence, median is 40.5

For mode, substituting the values,

  $z=81$

Hence, mode is 81