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Question
The weights of coffee in 70 jars is shown in the following table:
| Weight (in grams) |
Frequency |
| 200 – 201 | 13 |
| 201 – 202 | 27 |
| 202 – 203 | 18 |
| 203 – 204 | 10 |
| 204 – 205 | 1 |
| 205 – 206 | 1 |
Determine variance and standard deviation of the above distribution.
Solution
| Class-interval | `fi` | `x_i` | `d_i = x_i - A` | `f_i d_i` | `f_i d_i^2` |
| 200 – 201 | 13 | 200.5 | – 2 | – 26 | 52 |
| 201 – 202 | 27 | 201.5 | – 1 | – 27 | 27 |
| 202 – 203 | 18 | 202.5(A) | 0 | 0 | 0 |
| 203 – 204 | 10 | 203.5 | 1 | 10 | 10 |
| 204 – 205 | 1 | 204.5 | 2 | 2 | 4 |
| 205 – 206 | 1 | 205.5 | 3 | 3 | 9 |
| N = 70 | `sumf_i d_i` = – 38 | `sumf_i d_i^2` = 102 |
∴ Variance = `sigma^2 = (sumf_i d_i^2)/N - ((sumf_i d_i)/N)^2`
= `102/70 - ((-38)/70)^2`
= 1.457 – 0.292
= 1.165
∴ S.D. = `sigma = sqrt(1.165)`
= 1.08 g.
Hence, the required variance = 1.165 and S.D. = 1.08 g
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