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Consider the given data with frequency distribution

Which of the following option(s) is(are) TRUE?

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The median of the above data is 5

The mean of the above data is 6

The mean deviation about the median of the above data is 2.5

The mean deviation about the mean of the above data is 2.7

answer is A, B, C.

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Detailed Solution

$x_{i}$	$f_{i}$	$f_{i} x_{i}$	$f_{i} \| x_{i} - \bar{x} \|$	$f_{i} \| x_{i} - M \|$
3	5	15	15	10
4	4	16	8	4
5	4	20	4	0
8	2	16	4	6
10	2	20	8	10
11	3	33	15	18
	$\sum f_{i} = 20$	$\sum f_{i} x_{i} = 120$	Sum=54	Sum=48

(P) $M e a n (\bar{x}) = \frac{120}{20} = 6$

(Q) $M e d i a n = \frac{(10^{t h} + 11^{t h}) o b s e r v a t i o n}{2} = 5$

(R) $M . D . (\bar{x}) = \frac{\sum f_{i} | x_{i} - \bar{x} |}{\sum f_{i}} = \frac{54}{20} = 2.7$

(S) $M . D . (M) = \frac{\sum f_{i} | x_{i} - M |}{\sum f_{i}} = \frac{48}{20} = 2.4$

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