Question

A, B, C are three sets of values as given below:
A : 2, 3, 7, 1, 3, 2, 3
B : 7, 5, 9, 12, 5, 3, 8
C : 4, 4, 11, 7, 2, 3, 4
Which one 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. Median of C = Mode of C

Answer 1

The correct option is D Median of C = Mode of C

We know that,

$Mean=\frac{Sumofobservations}{Numberofobservations}$

$MeanofA=\frac{2+3+7+1+3+2+3}{7}=\frac{21}{7}=3$
$MeanofB=\frac{7+5+9+12+5+3+8}{7}=\frac{49}{7}=7$
$MeanofC=\frac{4+4+11+7+2+3+4}{7}=\frac{35}{7}=5$

For Median, sorting A in ascending order,
A : 1, 2, 2, 3, 3, 3, 7
Number of terms, n = 7 (Odd number of observations)
$\therefore$ Median = $4^{th}$ observation which is 3.

Now, sorting B in ascending order,
B : 3, 5, 5, 7, 8, 9, 12
Number of terms, n = 7 (Odd number of observations)
$\therefore$ Median = $4^{th}$ observation which is 7.

Similarly, sorting C in ascending order,
Number of terms, n = 7 (Odd number of observations)
C : 2, 3, 4, 4, 4, 7,11
$\therefore$ Median = $4^{th}$ observation which is 4.

The mode of a data set is the number that occurs most frequently.
So, mode of A = 3
mode of B = 5 and
mode of C = 4.

Hence from the above observations, we can conclude that
Mode of C = Median of C