Question

A group of six sixth-graders measure and record their heights. The heights (in inches) are shown below.52, 62, 53, 61, 55, 53Find the mean and the median of the heights.The mean is ?The median is ?PREV2021

Answer 1

Step 1

State an expression for the mean

`\bar{x}=(\Sigma fx)/(\Sigma f)`

Step 2

Find the mean

Substituting

Step 3

Find the median

`\text{The median is given by }(n)/(2)`

Where n = number of data = 6

`\begin{gathered} \text{Substituting for n we have} \\ \text{The median =}(6)/(2)\text{ = 3} \\ \text{This means the median is in the 3rd position or third item.} \end{gathered}`

Arranging the data in ascending order we have

52, 53, 53, 55, 61, 62

Hence from the front, the median is 53 and

From the back, the median is 55

Hence the median is given by

`\frac{53\text{ + 55}}{2}=(108)/(2)=54`

Hence, the mean is 56 and the median is 54