Mathematics
The weights of 50 apples were recorded as given below. Calculate the mean weight, to the nearest gram, by the step Deviation Method.
| Weight in grams | No.of apples |
|---|---|
| 80 – 85 | 5 |
| 85 – 90 | 8 |
| 90 – 95 | 10 |
| 95 – 100 | 12 |
| 100 – 105 | 8 |
| 105 – 110 | 4 |
| 110 – 115 | 3 |
Measures of Central Tendency
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Answer
We construct the following table, taking assumed mean a = 97.5. Here, c (width of each class) = 5.
| Weight in grams | No.of apples (fi) | Class mark (yi) | ui = (yi - a)/c | fiui |
|---|---|---|---|---|
| 80 – 85 | 5 | 82.5 | -3 | -15 |
| 85 – 90 | 8 | 87.5 | -2 | -16 |
| 90 – 95 | 10 | 92.5 | -1 | -10 |
| 95 – 100 | 12 | a=97.5 | 0 | 0 |
| 100 – 105 | 8 | 102.5 | 1 | 8 |
| 105 – 110 | 4 | 107.5 | 2 | 8 |
| 110 – 115 | 3 | 112.5 | 3 | 9 |
| Total | ∑ fi = 50 | ∑ fi ui = -16 |
By formula,
Hence, mean weight of the apples is 96 g.
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