Consider the following incomplete frequency distribution with a total frequency of 100: If the mean of the frequency distribution is 25, then what are the missing frequencies?Class Frequency 0-10 10 10-20 x 20-30 20 30-40 y
x = 25, y = 45
Since the total frequency is 100: \(10+x+20+y=100 \Rightarrow x+y=70\). Using class mid-points 5, 15, 25, 35 and mean = 25: \(\dfrac{10(5)+15x+20(25)+35y}{100}=25\), which gives \(550+15x+35y=2500 \Rightarrow 15x+35y=1950 \Rightarrow 3x+7y=390\). Substituting \(x=70-y\): \(3(70-y)+7y=390 \Rightarrow 210+4y=390 \Rightarrow y=45\), so \(x=25\). Hence option (d) is correct.
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