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Question

Calculate the mean, variance and standard deviation of the following frequency distribution.
Class: 1–10 10–20 20–30 30–40 40–50 50–60
Frequency: 11 29 18 4 5 3

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Solution

Let the assumed mean A = 25.
Class Mid-Valuesxi di=xi-A =xi-25 di2 Frequency fi fidi fidi2
1–10 5.5 −19.5 380.25 11 −214.5 4182.75
10–20 15 −10 100 29 −290 2900
20–30 25 0 0 18 0 0
30–40 35 10 100 4 40 400
40–50 45 20 400 5 100 2000
50–60 55 30 900 3 90 2700
N = fi = 70 fidi = −274.5 fidi2=12182.75

Mean = A+fidifi=25+-274.570=25-3.92=21.08

Variance = σ2=1Nfidi2-1Nfidi2=12182.7570--274.5702=174.02-15.37=158.65

Standard deviation = σ=158.65=12.6

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