Question

Are the mean and the median the exact same in this distribution? Why or why not?

Short answer

Yes, the mean and median are exactly same in this distribution$mean=median=5$

Step-by-step solution

Content Introduction

The mean is less than the median, which is frequently less than the mode, if the data distribution is skewed to the left. The median = the mean if the data distribution is symmetric.

Content Explanation

The mean is calculated using the below formula:

$Mean=\frac{\sum fx}{N}$

$$\begin{gathered} Mean=\frac{106}{21} \\ Mean=5 \end{gathered}$$

$$\begin{gathered} Median=\left(\frac{21+1}{2}\right) \\ Median={11}^{th}term \end{gathered}$$

Cumulative frequency lies in $x=5$

Therefore, mean is equal to median.