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Question
250 apples of a box were weighed and the distribution of masses of the apples is given in the following table:
| Mass (in grams) |
80 – 100 | 100 – 120 | 120 – 140 | 140 – 160 | 160 – 180 |
| Number of apples |
20 | 60 | 70 | x | 60 |
Find the value of x and the mean mass of the apples.
Solution
Given, total number of apples = 250
∴ 20 + 60 + 70 + x + 60 = 250
`\implies` x = 250 – 210 = 40
| Mass (in grams) C.I. |
Number apples (f) |
Mid value (x) |
d = (xi – A) |
f × d |
| 80 – 100 | 20 | 90 | –40 | –800 |
| 100 – 120 | 60 | 110 | –20 | –1200 |
| 120 – 140 | 70 | 130(A) | 0 | 0 |
| 140 – 160 | 40 | 150 | 20 | 800 |
| 160 – 180 | 60 | 170 | 40 | 2400 |
| `sumf` = 250 | `sumfd` = 1200 |
Now, mean `overlinex = A + (sumfd)/(sumf)`
= `130 + 1200/250`
= `130 + 24/5`
= 130 + 4.8
= 134.8
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