Chapter 1.3, Problem 92E

(a)

To determine

To calculate the median of the given data.

Answer to Problem 92E

Median = 7.5

Explanation of Solution

Given:

The dot plot:

  

Formula used:

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

Calculation:

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{\left(\frac{54}{2}\right)}^{\text{Th term}}+{\left(\frac{54}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{27}^{\text{Th term}}+{28}^{\text{Th term}}}{2}\\ =\frac{37+38}{2}\\ =37.5\end{array}$

(b)

To determine

To compare the mean and median without any calculation.

Explanation of Solution

Based on the given the dot plot, it is clearly visible that the data is skewed towards the left side or negatively skewed. When the data negatively skewed the value of mean is always less than the median. Therefore, Mean < Median.