Question

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

Short answer

The mean is $4.1$and is greater than the median, which is$4$.

Step-by-step solution

Given information

Given the distribution graph.

Explanation

The mean is calculated using the below formula:

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

x	Frequency, $f$	$fx$
3	8	24
4	4	16
5	2	10
6	2	12
7	1	7
	$N=17$	$\sum fx=69$

$\therefore \text{Mean}=\frac{69}{17}=4.1$

The median is calculated using the below formula:

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

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

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

Hence, the mean is greater than the median.