Find the mean and the standard deviation for the following data: x i 6 10 14 18 24 28 30 f i 2 4 7 12 8 4 3

The table is as below: x i f i f i x i x i - x ¯ 2 f i x i - x ¯ 2 6 2 12 169 338 10 4 40 81 324 14 7 98 25 175 18 12 216 1 12 24 8 192 25 200 28 4 112 81 324 30 3 90 121 363 n = ∑ f i = 40 ∑ f i x i = 760 ∑ f i x i - x ¯ 2 = 1736 By direct method, mean x ¯ = ∑ f i x i ∑ f i = 760 40 = 19 And, S.D σ = ∑ f i x i - x ¯ 2 ∑ f i = 1736 40 = 217 5 = 6 . 59

Find the mean, variance and standard deviation for the following frequency distribution: Classes 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 8 15 16 6

The table is as below: Classes Class mark x i f i d i = x i - A A = 25 u i = d i C C = 10 f i u i f i u i 2 0 - 10 5 5 - 20 - 2 - 10 20 10 - 20 15 8 - 10 - 1 - 8 8 20 - 30 25 15 0 0 0 0 30 - 40 35 16 10 1 16 16 40 - 50 45 6 20 2 12 24 ∑ f i = 50 ∑ f i u i = 10 ∑ f i u i 2 = 68 Thus, by step deviation method: Mean = A + ∑ f i u i ∑ f i × C = 25 + 10 50 × 10 = 27 Variance = σ 2 = ∑ f i u i 2 ∑ f i - ∑ f i u i ∑ f i 2 × C 2 = 68 50 - 10 50 2 × 100 = 1 . 36 - 0 . 04 × 100 = 1 . 32 × 100 = 132 So, S.D = σ = Variance = 132 = 11 . 49 .