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  • Following are the marks obtained by 9 students in a mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59 The mean deviation from the median is: A. 9 B. 10.5 C. 12.67 D. 14.76

Following are the marks obtained by 9 students in a mathematics test:

50, 69, 20, 33, 53, 39, 40, 65, 59
The mean deviation from the median is:
A. 9
B. 10.5
C. 12.67
D. 14.76

Answers (1)

Given that the marks obtained by 9 students in a mathematics test are 50, 69 , 20 ,33, 53, 39 ,40, 65, 59   As number of students =9 which is odd   

\\ \text{So median will be}\frac{9+1}{2}=5^{th}~term~ \\ \\ \text{~ Arranging these in ascending order, we get 20,33,39,40,50,53,59,65,69 } \\ \\ \text{~ So the }5^{th}\text{ term after arranging is 50 } \\ \\ \text{~ So, median is 50 } \\ \\ \text{This~can~be written in table form as, } \\

\begin{array}{|l|l|} \hline \text { Marks }\left(x_{i}\right) & \multicolumn{1}{|c|} {d_{i}=\mid x_{i}-\text {Median} \mid} \\ \hline 20 & 30 \\ \hline 33 & 17 \\ \hline 39 & 11 \\ \hline 40 & 10 \\ \hline 50 & 0 \\ \hline 53 & 3 \\ \hline 59 & 9 \\ \hline 65 & 15 \\ \hline 69 & 19 \\ \hline \text { Total } & =114 \\ \hline \end{array}

Hence Mean deviation becomes  \\ M.D=\frac{ \Sigma d_{i}}{n}=\frac{114}{9}=12.67 \\

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