Question

Construct a sample (with at least two different values in the set) of $4$ measurements whose mean, median, and mode are equal.

If this is not possible, indicate "Cannot create sample".

Answer 1

Finding median:

A set of numbers having at least two different values and $4$ measurements is the set $6,15,15,24$

Now median $=\frac{6+15+15+24}{4}=\frac{60}{4}=15$

$\therefore$There are even number of times so median is equal to mean of ${\frac{n}{2}}^{th}\&{\left({\frac{n}{2}}^{}+1\right)}^{th}$ term

$$\begin{gathered} =\frac{{{\displaystyle \frac{4}{2}}}^{th}+{\left({\displaystyle \frac{4}{2}}+1\right)}^{th}}{2}\text{term} \\ =\frac{2^{nd}\text{term}+3^{rd}\text{term}}{2} \\ =\frac{15+15}{3} \\ =\frac{30}{2}=15 \end{gathered}$$

Therefore, $15$ comes most of the time in the data.

So the mode is $15$

Thus, $mean=mode=median=15$