If the arithmetic mean and total frequency of the following distribution are 50 and 120 respectively, then find the value of f1 and f2:
| Class | Frequency |
| 0 – 20 | 17 |
| 20 – 40 | f1 |
| 40 – 60 | 32 |
| 60 – 80 | f2 |
| 80 – 100 | 19 |
WBBSE
Class X
Mathematics
Statistics
04 Mark
2023
| Class | x | f | fx |
| 0 – 20 | 10 | 17 | 170 |
| 20 – 40 | 30 | f1 | 30f1 |
| 40 – 60 | 50 | 32 | 1600 |
| 60 – 80 | 70 | f2 | 70f2 |
| 80 – 100 | 90 | 19 | 1710 |
| Total | 68 + f1 + f2 | 3480 + 30f1 + 70f2 |
Σf = 120
or, 68 + f1 + f2 = 120
or, f1 + f2 = 120 – 68
or, f1 + f2 = 52 — (1)
Σfx = mean × Σf
or, 3480 + 30f1 + 70f2 = 50 × 120
or, 30f1 + 70f2 = 2520
or, 3f1 + 7f2 = 252 — (2)
Solving (1) and (2), we get
f1 = 28
and f2 = 24
Hence, the values of f1 and f2 are 28 and 24.
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