Given are the observations of runs scored by batsmen between India - Sri Lanka combined. Find the mean deviation about mean for the scores of batsmen

$\begin{matrix} S c o r e & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 n u m b e r o f B a t s m e n & 12 & 18 & 27 & 20 & 17 & 6 \end{matrix}$

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Solution

The correct option is C
10

We write the midpoints of each given class and proceed as for a discrete frequency to find mean deviation.

$\begin{matrix} S c o r e & N o . o f B a t s m e n & M i d p o i n t s & f_{i} x_{i} & | x_{i} - ¯ x | & f_{i} | x_{i} - ¯ x | 10 - 20 & 2 & 15 & 30 & 30 & 60 20 - 30 & 3 & 25 & 75 & 20 & 60 30 - 40 & 8 & 35 & 250 & 10 & 80 40 - 50 & 14 & 45 & 630 & 0 & 0 50 - 60 & 8 & 55 & 440 & 10 & 80 60 - 70 & 3 & 65 & 195 & 20 & 60 70 - 80 & 2 & 75 & 150 & 30 & 60 40 & 1800 & 400 \end{matrix}$

$N = 7 \sum i = 1 f_{i} = 40, 7 \sum i = 1 f_{i} x_{i} = 1800, ¯ x = \frac{1}{N} 7 \sum i = 1 f_{i} x_{i} = \frac{1800}{40} = 45 \sum i = 1 7 f_{i} | x_{i} - ¯ x | = 400$

$M D (¯ x) = \frac{1}{N} \sum_{i = 1}^{7} f_{i} | x_{i} - ¯ x | = \frac{1}{40} (400) = 10$

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Q. Question 2
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Given are the observations of runs scored by batsmen between India - Sri Lanka combined. Find the mean deviation about mean for the scores of batsmen Score0−1010−2020−3030−4040−5050−60number ofBatsmen12182720176