Mathematics
The weights of 150 mangoes were recorded as given below :
| Weight in gms | Number of mangoes |
|---|---|
| 160-170 | 15 |
| 170-180 | 24 |
| 180-190 | 30 |
| 190-200 | 36 |
| 200-210 | 24 |
| 210-220 | 12 |
| 220-230 | 9 |
Calculate the mean weight (to the nearest gram) by step-deviation method.
Statistics
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Answer
i = Class size = 10.
In table below,
t =
| Class-interval | Frequency (f) | Mid-value (x) | d = x - A | t | f × t |
|---|---|---|---|---|---|
| 160-170 | 15 | 165 | -30 | -3 | -45 |
| 170-180 | 24 | 175 | -20 | -2 | -48 |
| 180-190 | 30 | 185 | -10 | -1 | -30 |
| 190-200 | 36 | A = 195 | 0 | 0 | 0 |
| 200-210 | 24 | 205 | 10 | 1 | 24 |
| 210-220 | 12 | 215 | 20 | 2 | 24 |
| 220-230 | 9 | 225 | 30 | 3 | 27 |
| Total | Σf = 150 | Σft = -48 |
By formula,
Mean = A +
= 195 +
= 195 -
= 195 - 3.2
= 191.8 ≈ 192 gms.
Hence, mean = 192 gms.
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