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Question
Calculate the mean and S.D. for the following data:
| Expenditure in Rs: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency: | 14 | 13 | 27 | 21 | 15 |
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Solution
| xpenditure(Rs) |
\[f_i\]
|
Midpoint \[\left( x_i \right)\]
|
\[f_i x_i\]
|
\[f_i x_i\]
|
\[\left( x_i - \bar{X} \right)^2\]
|
\[ f \left ( x_i - \bar{X} \right)^2\]
|
| 0−10 | 14 | 5 | 70 | - 21.1 | 445.21 | 6233.94 |
| 10−20 | 13 | 15 | 195 | - 11.1 | 123.21 | 1601.73 |
| 20−30 | 27 | 25 | 675 | -1.1 | 1.21 | 34.67 |
| 30−40 | 21 | 35 | 735 | 8.9 | 79.21 | 1663.41 |
| 40−50 | 15 | 45 | 675 | 18.9 | 357.21 | 5358.15 |
| \[\sum f_i = 90\] |
\[\sum f_i x_i = 2350\]
|
\[\sum f_i \left( x_i - \bar{X} \right)^2 = 14891 . 9\] |
Mean,
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