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Find the Mean Deviation from the Mean for the Data:Size2021222324frequency64514 - Mathematics

Find the mean deviation from the mean for the data:

Size 20 21 22 23 24
Frequency 6 4 5 1 4
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Solution

Size(xi) Frequency (fi) fi​xi \[\left| x_i - \bar{x} \right|\]
\[ = \left| x_i - 21 . 65 \right|\]

\[f_i \left| x_i - x \right|\]
\[ = f_i \left| x_i - 21 . 65 \right|\]
20 6 120 1.65 9.9
21 4 84 0.65 2.6
22 5 110 0.35 1.75
23 1 23 1.35 1.35
24 4 96 2.35 9.4
 
 

\[N = 20\]
 

\[\sum^n_{i = 1} f_i x_i = 433\]
 
 

\[\sum^n_{i = 1} f_i \left| x_i - x \right| = 25\]

\[\bar{x} = \frac{\sum^{n}_{i = 1} f_ix_i}{N} = \frac{433}{20} = 21 . 65\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{20} \times 25 = 1 . 25\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.2 | Q 4.4 | Page 11
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