Chapter 1.3, Problem 91E

(a)

To determine

To calculate the median of the given data.

Answer to Problem 91E

Median = 7.5

Explanation of Solution

Given:

  

Formula used:

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

Calculation:

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{\text{Th term}}+{\left(\frac{n}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{\left(\frac{50}{2}\right)}^{\text{Th term}}+{\left(\frac{50}{2}+1\right)}^{\text{Th term}}}{2}\\ =\frac{{25}^{\text{Th term}}+{26}^{\text{Th term}}}{2}\\ =\frac{7+8}{2}\\ =7.5\end{array}$

(b)

To determine

To compare the mean and median without any calculation.

Explanation of Solution

Based on the given the stem and leaf diagram, it is clearly visible that the data is skewed towards the right side or positively skewed. When the data positively skewed the value of mean is always greater than the median. Therefore, Mean > Median.