Question

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

Short answer

The mode is$3$and is less than the median, which is$4.$

Step-by-step solution

Given information

Given the distribution graph.

Explanation

The median is calculated using the below formula:

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

x	Frequency, f	Cumulative frequency, cf
3	8	8
4	4	12
5	2	14
6	2	16
7	1	17

$$\begin{gathered} \text{Median}=\text{size of}{\left(\frac{17+1}{2}\right)}^{th}\text{term} \\ =\text{size of}{9}^{\text{th}}\text{item} \\ =4\because \text{cumulative frequency}9\text{lies in}x=4 \end{gathered}$$

The mode is one that has a maximum frequency.

Therefore, the mode is $3$.

Hence, the mode is less than the median.