Question

$Set=(1,2,2,3,3,3,4,4,4,4)$. Evaluate the following expression for the given set of numbers.

$3\left(mean\right)\times 2\left(mode\right)-6\left(median\right)$.

Answer 1

Given set is $(1,2,2,3,3,3,4,4,4,4)$

Number of observations,$n=10$

$$\begin{gathered} Mean=\frac{sumofobservations}{numberofobservations} \\ Mean=\frac{30}{10} \\ Mean=3 \end{gathered}$$

Mode is the value that appears the maximum number of times.

Here mode $4$

Here n is even.

If n is even, then the median is given by the mean of observation and $\left[\right(\frac{n}{2})+1]$th observation.

Median = mean of 5th and 6th observation.

= $\frac{(3+3)}{2}$

= $2$

$$\begin{gathered} 3\left(mean\right)\times 2\left(mode\right)-6\left(median\right)=(3\times 3\times 2\times 4)-(6\times 3) \\ =72-18 \\ =54 \end{gathered}$$

Hence, $3\left(mean\right)\times 2\left(mode\right)-6\left(median\right)=54$