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Question
The weights (in kg) of 50 wrestlers are recorded in the following table:
| Weight (in kg) | 100 – 110 | 110 – 120 | 120 – 130 | 130 – 140 | 140 – 150 |
| Number of wrestlers |
4 | 14 | 21 | 8 | 3 |
Find the mean weight of the wrestlers.
Solution
We first find the class mark of each class and then proceed as follows.
| Weight (in kg) |
Number of wrestler `(bb(f_i))` |
Class marks `(bb(x_i))` |
Deviations `bb(d_i = x_i - a)` |
`bb(f_i d_i)` |
| 100 – 110 | 4 | 105 | – 20 | – 80 |
| 110 – 120 | 14 | 115 | – 10 | – 140 |
| 120 – 130 | 21 | a = 125 | 0 | 0 |
| 130 – 140 | 8 | 135 | 10 | 80 |
| 140 – 150 | 3 | 145 | 20 | 60 |
| `N = sumf_i = 50` | `sumf_i d_i = -80` |
∴ Assumed mean (a) = 125
Class width (h) = 10
And total observation (N) = 50
By assumed mean method,
Mean `(barx) = a + (sumf_i d_i)/(sumf_i)`
= `125 + ((-80))/50`
= 125 – 1.6
= 123.4 kg
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