Question

P, Q, R are three sets of values as given below:
P : 2, 3, 7, 1, 3, 2, 3
Q : 7, 5, 9, 12, 5, 3, 8
R : 4, 4, 11, 7, 2, 3, 4
Which one of the following statements is correct?

• A. Mean of P = Mode of R
• B. Median of Q = Mode of P
• C. Median of R = Mode of R
• D. Mean of R = Median of Q

Answer 1

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

We know that,

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

$MeanofP=\frac{2+3+7+1+3+2+3}{7}=\frac{21}{7}=3$
$MeanofQ=\frac{7+5+9+12+5+3+8}{7}=\frac{49}{7}=7$
$MeanofR=\frac{4+4+11+7+2+3+4}{7}=\frac{35}{7}=5$

For Median, sorting P in ascending order,
P : 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 Q in ascending order,
Q : 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 R in ascending order,
Number of terms, n = 7 (Odd number of observations)
R : 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 P = 3
mode of Q = 5 and
mode of R = 4.

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