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Consider the given data with frequency distribution
x_i 3 8 11 10 5 4
f_i 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 about the
mean of the above data is 3) 6
S) The mean deviation about the
median of the above data is 4) 2.7
5) 2.4
P Q R S
1) 3 2 4 5
2) 3 2 1 5
3) 2 3 4 1
4) 3 3 5 5

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Detailed Solution

x_i	f_i	c.f_i
3	5	5
4	4	9
5	4	13
8	2	15
10	2	17
11	3	20

$\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = 6 \Rightarrow P \to 3 N = 20, \frac{N}{2} = 10$
Median = Size of observation whose cumulative frequency just greater than or equal to 10= 5 $\Rightarrow Q \to 2$
Median deviation about mean $= \frac{{Σf}_{i} |x_{i} - \bar{x}|}{{Σf}_{i}} = 2.7 \Rightarrow R \to 4$
Mean deviation about median $= \frac{{Σf}_{i} |x_{i} - M|}{{Σf}_{i}} = 2.4 \Rightarrow S \to 5$

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