57. Find the missing frequencies f1, and f2 in the following distribution. It is given that median the distribution is rupees 41.50 and the

Questions

May 2023 2 11 Report

57. Find the missing frequencies f1, and f2 in the following distribution. It is given that median the distribution is rupees 41.50 and the total number of observations is 100.

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Answer:

Given that ∑ f i = 120 ∑fi=120 But from distribution table, ∑ f i = 17 ∑fi=17 + f1 + 32 + f2 + 19 = 68 + f1 + f2 ∴ 68 + f1 + f2 = 120 ⇒ f1 + f2 = 120 – 68 = 5 Hence, f1 + f2 = 52. … (1) But given that mean of given frequency distribution is 50. ∴ 3480 + 30 f 1 + 70 f 2 120 = 50 3480+30f1+70f2120=50 ⇒ 3480 + 30f1 + 70f2 = 6000 ⇒ 30 f1 + 70f2 = 6000 – 3480 = 2520. ⇒ 3f1 + 7f2 = 252. … (2) Now, multiplying equation (1) by 3, we get 3f1 + 3f2 = 156. … (3) Subtract equation (3) from equation (2), we get (3f1 + 7f2) – (3f1 + 3f2) = 252 – 156 = 96 ⇒ 4f2 = 96 ⇒ f2 = 96 4 = 24. 964=24. Now putting f2 = 24 in equation (1), we get f1 + 24 = 52 ⇒ f1 = 52 – 24 = 28. Hence, the missing frequencies are f1 = 28 and f2 = 24.