Chapter 10, Problem 9SGR

To determine

To calculate mean, median and mode

Answer to Problem 9SGR

Mean is 21, median is 19 and mode is 20.

Explanation of Solution

Given information:

The data set is,

6, 20, 55, 20, 7, 18

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,

  $z=Most\mathrm{Re}peatedValue$

Calculation:

Re-arranging the data in ascending order,

6,7,18,20,20,55

For mean, substituting the values,

  $\overline{x}=\frac{6+7+18+20+20+55}{6}$

So,

  $\overline{x}=\frac{126}{6}$

On solving,

  $\overline{x}=21$

Hence, mean is 21

For median, substituting the values,

  $M=\frac{{(\frac{6}{2})}^{th}+{(\frac{6}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{3^{rd}+4^{th}}{2}$

Substituting the values,

  $M=\frac{18+20}{2}$

On solving,

  $M=19$

Hence, median is 19.

For mode, substituting the values,

  $z=20$

Hence, mode is 20.