Question -
Answer -
The following was the distribution of mangoesaccording to the number of boxes.
| Number of mangoes | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
| Number of boxes | 15 | 110 | 135 | 115 | 25 |
Find the mean numberof mangoes kept in a packing box. Which method of finding the mean did you choose?
Solution:
Since, the given data is not continuous so weadd 0.5 to the upper limit and subtract 0.45 from the lower limit as the gapbetween two intervals are 1
Here, assumed mean (A) = 57
Class size (h) = 3
Here, the step deviation is used because thefrequency values are big.
| Class Interval | Number of boxes (fi) | Mid-point (xi) | di = xi – A | fidi |
| 49.5-52.5 | 15 | 51 | -6 | 90 |
| 52.5-55.5 | 110 | 54 | -3 | -330 |
| 55.5-58.5 | 135 | 57 = A | 0 | 0 |
| 58.5-61.5 | 115 | 60 | 3 | 345 |
| 61.5-64.5 | 25 | 63 | 6 | 150 |
| Sum fi = 400 | | | Sum fidi = 75 |
The formula to find out the Mean is:
Mean = x̄ = A +h ∑fidi /∑fi
= 57 + 3(75/400)
= 57 + 0.1875
= 57.19
Therefore, the mean number of mangoes kept ina packing box is 57.19