Question

Determine the mean, mode and the median of the data:
$23,2,42,6,36,11,29,9,15$

Answer 1

Let us rewrite the given data in the ascending order,

$2,6,9,11,15,23,29,36,42$

$\begin{array}{cc}\text{Mean}& =\frac{\left(23+2+42+6+36+11+29+9+15\right)}{9}\\ & =\frac{173}{9}\\ & =19.22\end{array}$

As there are $9$ terms in total that is odd hence, ${\left(\frac{n+1}{2}\right)}^{th}$ term will be the median of the data.

$\text{Median}=15$

By using the relation between mean, mode and median is,

$\begin{array}{cc}\text{Mode}+2\text{Mean}& =3\text{Median}\\ \text{Mode}& =3\times 15-2\times 19.22\\ & =45-38.44\\ & =6.56\end{array}$