Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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In 22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between ¯ X − M.D. and ¯ X + M.D, where M.D. is the mean deviation from the mean. - Mathematics

In  22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between 

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.

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Solution

Let \[\bar{x}\]   be the mean of the data set.

\[\bar{ x } = \frac{22 + 24 + 30 + 27 + 29 + 31 + 25 + 28 + 41 + 42}{10} = 29 . 9\]

\[x_i\]
\[\left| d_i \right| = \left| x_i - 29 . 9 \right|\]
22 7.9
24 5.9
30 0.1
27 2.9
29 0.9
31 1.1
25 4.9
28 1.9
41 11.9
42 12.1
Total 48.8

\[MD = \frac{1}{10} \times 48 . 8 = 4 . 88\]

\[\bar{ x }  - M . D . = 29 . 9 - 4 . 88 = 25 . 02, \]

\[\text{ and } \bar {  x } + M . D . = 29 . 9 + 4 . 88 = 34 . 78\]

There are 5 observations between 25.02 and 34.78.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.1 | Q 5.2 | Page 6
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