Question

Describe the relationship between the mode and the median of this distribution.

Short answer

The data distribution is symmetric because$median=mode$

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. If the distribution of data is skewed to the right, the mode is generally less than the median, which is less than the mean. The mode = the median = the mean if the data distribution is symmetric.

Content Explanation

The median is calculated using the below formula:

$\mathrm{Median}={\left(\frac{\mathrm{N}+1}{2}\right)}^{\mathrm{th}}\mathrm{term}$

from the above table, $N=21$

Therefore,

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

Cumulative frequency ${11}^{th}$lies in $x=5$

The mode is one that has a maximum frequency.

Therefore, the mode is$5.$