Chapter 12.3, Problem 32SR

To determine

To calculate:

The measure of central tendency that best represent the data with justification and also calculate the measure

Answer to Problem 32SR

The median class best represent the data and its calculated value is 13.

Explanation of Solution

Given information:

The pound of food brought by the classes are represented by the data set is 8, 12, 18, 25, 21, 5, 10, 14

Formula used:

Median = ${\left(\frac{n}{2},\frac{n}{2}+1\right)}^{th}$ term = $\frac{n^{th}\text{ term}}{2}$

Calculation:

Since, here is no big gap in the middle of the data and the data set has outliers so median will be best to represent the data.

At first all the number are arranged in ascending order,

5, 8, 10, 12, 14, 18, 21, 25

Now, there are total 8 number that means $n=8$ which is even so the median is calculated as,

Median = $\left(\frac{n}{2},\frac{n}{2}+1\right)$ term

  $\begin{array}{l}={\left(\frac{8}{2},\frac{8}{2}+1\right)}^{th}\text{ term}\\ ={\left(4,5\right)}^{th}\text{ term}\end{array}$

So, the median is,

  $\begin{array}{l}\frac{\left(4^{th}+5^{th}\right)\text{term}}{2}\\ =\frac{12+14}{2}\\ =\frac{26}{2}\\ =13\end{array}$

Therefore, the median is 13