Chapter 13.3, Problem 22SR

To determine

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

Answer to Problem 22SR

Mean $=18.3$ , Median $=18$ , Mode $=16,18,20$

Explanation of Solution

Given information:

The set of data $16,16,16,17,18,18,18,19,19,20,20,20,21$

Formula used:

Mean $=\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{n}$ ,

Median $={(\frac{n+1}{2})}^{th}term$ , if n is odd.

Median $=\frac{{(\frac{n}{2})}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$ , if n is even.

Mode $=$ most frequently occurring data

n $=$ number of terms.

Calculation:

The set of data $16,16,16,17,18,18,18,19,19,20,20,20,21$

Here, $n=13$ , which is odd.

Mean

  $\begin{array}{l}=\frac{16,16,16,17,18,18,18,19,19,20,20,20,21}{13}\\ =\frac{238}{13}\\ =18.307\end{array}$

Rounding to nearest tenth, Mean $=18.3$

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

  $\begin{array}{l}$ ={(\frac{13+1}{2})}^{th}term$=7^{th}term\\ =18\end{array}$

In the data set 16,18 and 20 each occurred 3 times.

Thus, Mode $=16,18,20$

Conclusion:

Mean $=18.3$ , Median $=18$ , Mode $=16,18,20$