EX 13.3 (Question: 2)

EX 13.3 (Question: 2) If the median of the distribution given below is 28.5, find the values of 𝑥 and 𝑦.Class interval Frequency 0 - 10 5 10 - 20 x 20 - 30 20 30 - 40 15 40 - 50 y 50 - 60 5 Total 60

Solution: Given median = 28.5, total frequency = 60, 5 + 𝑥 + 20 + 15 + 𝑦 + 5 = 60  ⟹  𝑥 + 𝑦 = 15Median class = 20 – 30, Using median formula: Median = 𝑙 + ( "n/2−F" /"𝑓" )"×h" Where: 𝑙 = 20, 𝑛/2 = 30, 𝐹 = 5 + 𝑥, 𝑓 = 20, ℎ = 10 28.5 = 20 + ("(30−(5+𝑥)" /20)"× 10" 8.5 = (25−𝑥)/2 "17= 25−x " "𝑥= 8 " Using 𝑥 + 𝑦 = 15:  8 + 𝑦 = 15  ⟹  𝑦 = 7

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