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Find the Mean, Mode, S.D. and Coefficient of Skewness for the Following Data: Year Render:102030405060no. of Persons (Cumulative):1532517897109 - Mathematics

Find the mean, mode, S.D. and coefficient of skewness for the following data: 

Year render: 10 20 30 40 50 60
No. of persons (cumulative): 15 32 51 78 97 109
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Solution

Year render No. of persons (cumulative)
 

\[f_i\]
 

\[u_i = \frac{x_i - 35}{10}\]
 

\[f_i u_i\]
 

\[{u_i}^2\]
 

\[f_i {u_i}^2\]
10 15 15
- 2.5
- 37.5
6.25 93.75
20 32 17
- 1.5
- 25.5
2.25 38.25
30 51 19
- 0.5
- 9.5
0.25 4.75
40 78 27 0.5 13.5 0.25 6.75
50 97 19 1.5 28.5 2.25 42.75
60 109 12 2.5 30 6.25 75
   
 

\[\sum f_i = N = 109\]
 
 

\[\sum f_i u_i = - 0 . 5\]
 
 

\[\sum f_i {u_i}^2 = 261 . 25\]

\[\bar{X} = A + h\left( \frac{\sum f_i u_i}{N} \right)\]

\[ = 35 + 10\left( \frac{- 0 . 5}{109} \right)\]

\[ = 34 . 96 \text{ years } \]

\[\sigma^2 = h^2 \left[ \frac{\sum f_i {u_i}^2}{N} - \left( \frac{\sum f_i u_i}{N} \right)^2 \right]\]

\[ = 100\left[ \frac{261 . 25}{109} - \frac{0 . 25}{11881} \right]\]

\[ = 100 \times 2 . 396\]

\[ = 239 . 6\]

\[\sigma = \sqrt{239 . 6}\]

\[ = 15 . 47 \text{ years } \]

Coefficient of skewness = Mean - Mode

                                    = 34.96 - 40
 
                                    = -5.04
 
  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 32.5 | Q 3 | Page 38
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