Mathematics
The mean of the following frequency distribution is 50, but the frequencies f1 and f2 in class 20-40 and 60-80 respectively are not known. Find these frequencies.
Class | Frequencies |
---|---|
0-20 | 17 |
20-40 | f1 |
40-60 | 32 |
60-80 | f2 |
80-100 | 19 |
Given that the sum of frequencies is 120.
Statistics
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Answer
Class | Frequencies (f) | Class marks (x) | fx |
---|---|---|---|
0-20 | 17 | 10 | 170 |
20-40 | f1 | 30 | 30f1 |
40-60 | 32 | 50 | 1600 |
60-80 | f2 | 70 | 70f2 |
80-100 | 19 | 90 | 1710 |
Total | Σf = f1 + f2 + 68 | Σfx = 3480 + 30f1 + 70f2 |
Given,
Σf = 120
⇒ f1 + f2 + 68 = 120
⇒ f1 + f2 = 120 - 68
⇒ f1 + f2 = 52
⇒ f1 = 52 - f2 ……….(1)
By formula,
Mean =
Substituting values we get :
Substituting value of f1 from equation (1) in above equation, we get :
⇒ 6000 = 3480 + 30(52 - f2) + 70f2
⇒ 6000 = 3480 + 1560 - 30f2 + 70f2
⇒ 6000 = 5040 + 40f2
⇒ 40f2 = 6000 - 5040
⇒ 40f2 = 960
⇒ f2 = = 24.
⇒ f1 = 52 - f2 = 52 - 24 = 28.
Hence, f1 = 28 and f2 = 24.
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