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Calculate the Mean Deviation About the Median of the Observation: 38, 70, 48, 34, 63, 42, 55, 44, 53, 47 - Mathematics

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प्रश्न

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

 
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उत्तर

Formula used for mean deviation:

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]

\[Here, \]

\[ d_i = x_i - M\]

 M = Median

v) Arranging the data in ascending order:
34, 38, 42, 44, 47, 48, 53, 55, 63, 70

Here,

\[n = 10\].

Also, median is the AM of the fifth and the sixth observation.

\[Median, M = \frac{47 + 48}{2} = 47 . 5\]

xi
 
\[\left| d_i \right| = \left| x_i - M \right|\]
38 9.5
70 22.5
48 0.5
34 13.5
63 15.5
42 5.5
55 7.5
44 3.5
53 5.5
47 0.5
Total 84

\[MD = \frac{1}{10} \times 84 = 8 . 4\]

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पाठ 32: Statistics - Exercise 32.1 [पृष्ठ ६]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 32 Statistics
Exercise 32.1 | Q 1.5 | पृष्ठ ६

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