The mean of the folowing is 62.8 and the sum of all the frequencies is 50. find the missing frequency `f_1 and f_2`
Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |
Freq | 5 | `f_1` | 10 | `f_2` | 7 | 8 |
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Solution
class | Freq (f) | Mid value | fx |
0-20 | 5 | 10 | 50 |
20-40 | `f_1` | 30 | 30`f_1` |
40-60 | 10 | 50 | 500 |
60-80 | `f_2` | 70 | 70`f_2` |
80-100 | 7 | 90 | 630 |
100-120 | 8 | 110 | 880 |
total | 30+`f_1`+`f_2` | 2060+30`f_1`+70`f_2` |
Now, `∑ f= 30+f_1+f_2 and ∑ fx=2060+30f_1+70f_2` .........(1)
∑ f=50; mean=62.8 ...........(2)
From(1)
`30+f_1+f_2=50`
`f_1+f_2=20`.........(3)
Using (1) and (2)
`Mean=(2060+30f_1+70f_2)/50`
`62.8=(2060+30fi+70f_2)/50`
`2060+30f_1+70f_2=62.8xx50`
`2060+30f_1+70f_2=3140`
`30f_1+70f_2=1080`
`3f_1+7f_2=108`........(4)
From (3)and (4)
`f_1=8`
`f_2=12`
Concept: Concept of Median
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