Question
The marks (out of 50) of 5 students are: 10, 14, 18, x,
26. The mean is 18. Find x and the standard deviation.Solution
Mean = 18 β total sum = 5 Γ 18 = 90 Known sum = 10 + 14 + 18 + 26 = 68 So x = 90 β 68 = 22 Data: 10, 14, 18, 22, 26; mean = 18 Deviations from mean: 10 β 18 = β8 14 β 18 = β4 18 β 18 = 0 22 β 18 = 4 26 β 18 = 8 Squares: 64, 16, 0, 16, 64 Sum of squares = 160 Standard deviation (population) = β(Ξ£(dΒ²)/n) = β(160/5) = β32 = 4β2.
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