Question

For which set of numbers do the mean, median and mode have the same value?

• A. $2,2,2,4$
• B. $1,3,3,3,5$
• C. $1,1,2,5,6$
• D. $1,1,1,2,5$

Answer 1

The correct option is B

$1,3,3,3,5$

Explanation for incorrect option

Considering the first set of numbers,

We have,

$2,2,2,4$

So, mean will be =$\frac{2+2+2+4}{4}=\frac{10}{4}=2.5$

For determining we will arrange the number in ascending order

So, the order will be $2,2,2,4$

As here,$n=4,$ even,

So, median will be =$\frac{2+2}{2}=2$

As, here $mean\ne median$

So, the condition given in the question is not satisfied.

Now considering second set of numbers:

We have set of observations $1,3,3,3,5,$

Mean of the above observation is $\frac{1+3+3+3+5}{5}=\frac{15}{5}=3$

The set of observations is ascending order is $1,3,3,3,5$

Here the total number of observations are $5$ which is odd.

Therefore, median =${\left(\frac{5+1}{2}\right)}^{\text{th}}$ observation $=3rd$ observation $=3$

The mode is that observation which is repeated maximum number of times.

Here the observation $3$ is repeated maximum $3$ - times

So, the mode is also $3.$

So, for the given set of numbers $mean=median=mode$.

Hence, option (b) is the correct choice.

Explanation for incorrect option(s)

(c)mean $=\frac{1+1+2+5+6}{5}=\frac{15}{2}=7.5$

median $2$

As, here $mean\ne median$

So, the condition given in the question is not satisfied.

(d)mean $=\frac{1+1+1+2+5}{5}=\frac{10}{2}=5$

median $1$

As, here $mean\ne median$

So, the condition given in the question is not satisfied.