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Find the Mean Deviation from the Mean for the Data:Classes0-100100-200200-300300-400400-500500-600600-700700-800frequencies489107543 - Mathematics

Find the mean deviation from the mean for the data:

Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
Frequencies 4 8 9 10 7 5 4 3

 

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Solution

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

Classes 
\[f_i\]
Midpoints
 

\[x_i\]
 

\[f_i x_i\]
 

\[\left| x_i - X \right|\]
=
 

\[\left| x_i - 358 \right|\]
 

\[f_i \left| x_i - X \right|\]
0−100 4 50 200 308 1232
100−200 8 150 1200 208 1664
200−300 9 250 2250 108 972
300−400 10 350 3500 8 80
400−500 7 450 3150 92 644
500−600 5 550 2750 192 960
600−700 4 650 2600 292 1168
700−800 3 750 2250 392 1176
 
 

\[\sum^8_{i = 1} f_i = 50\]
 
 

\[\sum^8_{i = 1} f_ix_i= 17900\]
  \[\sum^8_{i = 1} f_i \left| x_i - X \right| = 7896\]

 

 

\[N = \sum^6_{i = 1} f_i = 50\] and 

\[\sum^6_{i = 1} f_i x_i = 17900\]

\[\bar{ X }  = \frac{\sum^{8} _{i = 1} f_i x_i}{\sum ^8_{i = 1} f_i} = \frac{17900}{50} = 358\]

\[\therefore \text{ Mean deviation } = \frac{1}{N} \sum^8_{i = 1} f_i \left| x_i - X \right|\]
\[ = \frac{7896}{50}\]
\[ = 157 . 92\]

  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 2.1 | Page 16
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