Chapter 10, Problem 2PT

To determine

To calculate mean, median and mode.

Answer to Problem 2PT

Mean is 30.38, median is 31.5, mode is 30 and 41.

Explanation of Solution

Given information:

The data set is,

{30, 22, 38, 41, 33, 41, 30, 24}

Formula used:

Mean is,

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

Median is,

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

Mode is the maximum value or the most repeated value,

  $z=Most\mathrm{Re}peatedValue$

Calculation:

For mean, substituting the values in the formula,

  $\overline{x}=\frac{30+22+38+41+33+41+30+24}{8}$

So,

  $\overline{x}=\frac{259}{8}$

On solving,

  $\overline{x}=32.38$

Hence, mean is 32.38

Re-arranging the data set in an ascending order,

22, 24, 30, 30, 33, 38, 41, 41

For median, substituting the values in the formula,

  $M=\frac{\frac{{(8)}^{th}}{2}+{(\frac{8}{2}+1)}^{th}}{2}$

On solving,

  $M=\frac{4^{th}+5^{th}}{2}$

Substituting the values,

  $M=\frac{30+33}{2}$

On solving,

  $M=31.5$

Hence, median is 31.5

For mode, there are 2 values repeating equally, the data set is bimodal.

Substituting the value,

$z=30$ and $41$

Hence, mode is 30 and 41