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Find the Mean Deviation from the Mean for the Data:Classes95-105105-115115-125125-135135-145145-155frequencies91316263012 - Mathematics

Find the mean deviation from the mean for the data:

Classes 95-105 105-115 115-125 125-135 135-145 145-155
Frequencies 9 13 16 26 30 12

 

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Solution

We will compute the mean deviation from the mean in the following way: 

Classes  Frequency 
\[f_i\]
Midpoints
\[x_i\]
 

\[f_i x_i\]
 

\[\left| x_i - X \right|\]
=
\[\left| x_i - 128 . 58 \right|\]
\[f_i \left| x_i - X \right|\]
95−105 9 100 900 28.58 257.22
105−115 13 110 1430 18.58 241.54
115−125 16 120 1920 8.58 137.28
125−135 26 130 3380 1.42 36.92
135−145 30 140 4200 11.42 342.6
145−155 12 150 1800 21.42 257.04
 
 

\[\sum^6_{i = 1} f_i = 106\]
 
 

\[\sum^6_{i = 1} f_i x_i = 13630\]
  \[\sum^8_{i = 1}|  f_i x_i  |- \bar{x}= 1272.6\]

 

\[N = \sum^6_{i = 1} f_i = 106\] and

\[\sum^6_{i = 1} f_i x_i = 13630\]

\[\therefore X = \frac{\sum^6_{i = 1} f_i x_i}{\sum^6_{i = 1} f_i}\]

\[ = \frac{13630}{106}\]

\[ = 128 . 58\]

\[\therefore \text{ Mean deviation } = \frac{1}{N} \sum^8_{i = 1} f_i \left| x_i - X \right|\]

\[ = \frac{1272 . 6}{106}\]

\[ = 12 . 005\]

  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 32.3 | Q 2.2 | Page 16
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