WBBSEClass XMathematicsStatistics04 Mark2023 Moderate

QQuestion

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

Exam-ready answer • 04 Mark

Answer

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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