Question

$A,B,C$ are three sets of values of $x$:

$$\begin{gathered} A:2,3,7,1,3,2,3 \\ B:7,5,9,12,5,3,8 \\ C:4,4,11,7,2,3,4 \end{gathered}$$

Which of the following statements is correct?

• A. Mean of A= Mode of C
• B. Mean of C= Median of B
• C. Median of B= Mode of A
• D. Mean, Median and Mode of A are equal.

Answer 1

The correct option is D

Mean, Median and Mode of A are equal.

Step 1: Calculation of mean:

As we know,

Mean of the data $=\frac{Sumofalltheobservations}{Numberofobervations}$

Mean of $A=\frac{2+3+7+1+3+2+3}{7}=\frac{21}{7}=3$

Step 2: Calculation of median:

Median of A: $1,2,2,3,3,3,7$

Here, $n=7$

As, value of $n$is odd,

So, median will be $\frac{n+1}{2}thterm$

$\therefore Median=\frac{7th+1}{2}=\frac{8th}{2}=4thobservation=3$

Step 3: Calculation of Mode:

$Mode=3$ (As the frequency of 3 is most)

So, here, the mean, median, and mode of A are the same.

Hence, option (d) is the correct choice.