Question

Find the mean and median of all the positive factors of $72$?

Answer 1

Step $1$: Compute the required mean.

Factors of $72$ are : $1,2,3,4,6,8,9,12,18,24,36,72$

We know that,

$\text{Mean=}\frac{\text{Sum of all the observations}}{\text{Total number of observations}}$

Mean calculation:

$\Rightarrow Mean=\frac{1+2+3+4+6+8+9+12+18+24+36+72}{12}=\frac{195}{12}=16.25$

Step $2$: Compute the required median.

We know that,

Median $\text{M}=\frac{{\left({\displaystyle \frac{n}{2}}\right)}^{t{h}_{}}+{\left({\displaystyle \frac{n}{2}}+1\right)}^{th}}{2}$

Where, $n$ is total number of terms

Median calculation:

$$\begin{gathered} \text{M}=\frac{1}{2}\left(6^{th}+7^{th}\right) \\ \Rightarrow \text{M}=\frac{1}{2}\left(8+9\right) \\ \Rightarrow \text{M}=8.5 \end{gathered}$$

Hence, the mean is $16.25$ and the median is $8.5$.