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Question
Find the standard deviation for the following data:
| x : | 3 | 8 | 13 | 18 | 23 |
| f : | 7 | 10 | 15 | 10 | 6 |
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Solution
|
\[x_i\]
|
\[f_i\]
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\[f_i x_i\]
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\[\left( x_i - \bar{X} \right)\]
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\[\left( x_i - \bar{X} \right)^2\]
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\[f_i \left( x_i - \bar{X} \right)^2\]
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| 3 | 7 | 21 | −9.79 | 95.84 | 670.88 |
| 8 | 10 | 80 | −4.79 | 22.94 | 229.4 |
| 13 | 15 | 195 | 0.21 | 0.04 | 0.6 |
| 18 | 10 | 180 | 5.21 | 27.14 | 271.4 |
| 23 | 6 | 138 | 10.21 | 104.24 | 625.44 |
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\[\sum f_i = 48\]
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\[\sum f_i x_i = 614\]
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\[\sum f_i \left( x_i - \bar{X} \right)^2 = 1797 . 32\]
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Variance,
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