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Find the Mean Deviation from the Mean for the Data:Xi1030507090fi42428168 - Mathematics

Find the mean deviation from the mean for the data:

xi 10 30 50 70 90
fi 4 24 28 16 8
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Solution

xi fi fi​xi
 

\[\left| x_i - \bar{x} \right|\]
 

\[f_i \left| x_i - 50 \right|\]
10 4 40 40 160
30 24 720 20 480
50 28 1400 0 0
70 16 1120 20 320
90 8 720 40 320
 
 

\[N = 80\]
 

\[\sum^n_{i = 1} f_i x_i = 4000\]
 
 

\[\sum^n_{i = 1} f_i \left| x_i - 50 \right| = 1280\]
\[\bar{ x } = \frac{\sum ^n _{i = 1} f_ix_i}{N} = \frac{4000}{80} = 50\]
\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i -\bar{ x } \right| = \frac{1}{80} \times 1280 = 16\]
  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 32.2 | Q 4.3 | Page 11
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