Step 1
State an expression for the mean
[tex]\bar{x}=\frac{\Sigma fx}{\Sigma f}[/tex]Step 2
Find the mean
Substituting
[tex]\bar{x}(\operatorname{mean})\text{ =}\frac{336}{6\text{ }}=56[/tex]Step 3
Find the median
[tex]\text{The median is given by }\frac{n}{2}[/tex]Where n = number of data = 6
[tex]\begin{gathered} \text{Substituting for n we have} \\ \text{The median =}\frac{6}{2}\text{ = 3} \\ \text{This means the median is in the 3rd position or third item.} \end{gathered}[/tex]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
[tex]\frac{53\text{ + 55}}{2}=\frac{108}{2}=54[/tex]Hence, the mean is 56 and the median is 54
