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Consider the following frequency distribution of 44 students
$x_{i}$
3
9
17
23
27
$f_{i}$
8
10
2
9
5
Match entries in column-I with their corresponding values column-II
Column–I
Column–II
A)
Mean of the given distribution is
P)
10
B)
Median of the given distribution
Q)
15
C)
Mean deviation about mean of the given distribution is
R)
17
D)
Mean deviation about median of the given distribution is
S)
$\frac{74}{11}$

T)
$\frac{78}{11}$

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A–Q, B–P, C–T, D–P

A–Q, B–R, C–T, D–S

A–T, B–R, C–P, D–S

A–T, B–P, C–Q, D–S

answer is B.

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Detailed Solution

$x_{i}$	$f_{i}$	$\sum f_{i} x_{i}$	$f_{i} \| (x_{i} - \bar{x}) \|$	$f_{i} \| x_{i} - M e d i a n \|$
3	8	24	96	2
9	10	90	60	80
17	12	204	24	0
23	9	207	72	54
27	5	132	60	50
	$\sum f_{i} = 44$	$\sum f_{i} x_{i} = 660$	$\sum f_{i} \| x_{i} - M \| = 132$	$\sum f_{i} \| x_{i} - M e d i a n \| = 296$

Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{660}{44} = 15$
Median = 17
Mean deviation about mean $= \frac{\sum f_{i} | x_{i} - \bar{x} |}{\sum f_{i}} = \frac{312}{44} = 7.09$
Mean deviation about median $= \frac{\sum f_{i} | x_{i} - M e d i a n |}{\sum f_{i}} = \frac{296}{44} = 6.727$

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