Question

Consider the given data with frequency distribution

xi	3	8	11	10	5	4
fi	5	2	3	2	4	4

Match each entry in List-I to the correct entries in List-II.
| List-I| | List-II
---|---|---|---
(P)| The mean of the above data is| (1)| 2.5
(Q)| The median of the above data is| (2)| 5
(R)| The mean deviation from the mean of the above data is| (3)| 6
(S)| The mean deviation from the median of the above data is| (4)| 2.7
| | (5)| 2.4

The correct option is:

• A. (P)$\rightarrow$(3),(Q)$\rightarrow$(2),(R)$\rightarrow$(4),(S)$\rightarrow$(5)
• B. (P)$\rightarrow$(3) (Q)$\rightarrow$(2) (R)$\rightarrow$(1) (S)$\rightarrow$(5)
• C. (P)$\rightarrow$(2) (Q)$\rightarrow$(3) (R)$\rightarrow$(4) (S)$\rightarrow$(1)
• D. (P)$\rightarrow$(3) (Q)$\rightarrow$(3) (R)$\rightarrow$(5) (S)$\rightarrow$(5)

Answer 1

Answer: (A)

(P)$\rightarrow$(3),(Q)$\rightarrow$(2),(R)$\rightarrow$(4),(S)$\rightarrow$(5)

Answer 2

The correct answer is (A)
Mean = $\frac{3\times5+8\times2+11\times3+10\times2+5\times4+4\times 4}{5+2+3+2+4+4}$
$= \frac{15+16+33+20+20+16}{20}=\frac{120}{20}=6$
Median = $\frac{1}{2}$(10th and 11th observations)
$=\frac{1}{2}(5+5)$
Mean deviation about the mean = $\frac{54}{20}= 2.7$
Mean deviation about median = $\frac{48}{20}=2.4$