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Question
Calculate mean, variation and standard deviation of the following frequency distribution:
| Classes | Frequency |
| 1 – 10 | 11 |
| 10 – 20 | 29 |
| 20 – 30 | 18 |
| 30 – 40 | 4 |
| 40 – 50 | 5 |
| 50 – 60 | 3 |
Solution
Let A, the assumed mean, be 25.5.
Here h = 10
| Classes | `x_i` | `y_i = (x_i - 25.5)/10` | `f_i` | `f_iy_i` | `f_iy_i^2` |
| 1 – 10 | 5.5 | –2 | 11 | –22 | 44 |
| 10 – 20 | 15.5 | –1 | 29 | –29 | 29 |
| 20 – 30 | 25.5 | 0 | 18 | 0 | 0 |
| 30 – 40 | 35.5 | 1 | 4 | 4 | 4 |
| 40 – 50 | 45.5 | 2 | 5 | 10 | 20 |
| 50 – 60 | 55.5 | 3 | 3 | 9 | 27 |
| 70 | –28 | 124 |
x' = `(f_i y_i)/(f_i) = (-28)/70 = - 0.4`
Mean = `barx` = 25.5 + (–10)(0.4) = 21.5
Variance `(sigma^2) = h/N sqrt(N f_iy_i^2 - (g_iy_1)^2)^2`
= `(10 xx 0)/(70 xx 70) [70(124) - (-28)^2]`
= `(70(124))/(7 xx 7) - (28 xx 28)/(7 xx 7)`
= `1240/7 - 16`
= 161
S.D. `(sigma) = sqrt(161)` = 12.7
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