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Two groups: best, consistent, SE of difference

Short answer

Group B mean 43.19, SD 13.98; Group A mean 30.19, SD 12.88. Group B is best (higher mean) and more consistent (CV 32.38% vs 42.66%). Standard error of difference = √(165.83/32 + 195.58/32) ≈ 3.36.

The scores of randomly selected 32 students of two groups on Probability and Statistics are: Group A: 50 37 13 37 45 9 11 34 24 6 13 24 32 32 24 40 33 45 37 38 33 32 46 32 46 21 32 4 45 16 43 32 Group B: 56 74 50 43 39 24 55 35 72 32 45 59 47 36 34 32 40 53 55 18 32 42 49 32 41 33 14 60 60 34 38 48 a) Which group is best? b) Which group is more consistent? c) Find standard error of difference of their means.

Compare the groups by their means (which is better) and by the coefficient of variation CV = (s / x̄) × 100 (which is more consistent). Both groups have n = 32.

Calculations

Group AGroup B
Σx9661382
Σx²34,30265,748
Mean x̄30.1943.19
Sxx = Σx² − (Σx)²/n5140.96062.9
s² = Sxx/31165.83195.58
s12.8813.98
CV42.66 %32.38 %

Working for Group A: x̄ = 966/32 = 30.1875; Sxx = 34,302 − 966²/32 = 5140.875; s² = 5140.875/31 = 165.83.

a) Best group

Group B is better because its average score (43.19) is higher than that of A (30.19).

b) More consistent group

Group B is more consistent because its CV (32.38 %) is smaller than the CV of A (42.66 %).

c) Standard error of the difference of means

SE(x̄A − x̄B) = √( sA²/nA + sB²/nB )
             = √( 165.83/32 + 195.58/32 )
             = √( 5.182 + 6.112 )
             = √11.294
             = 3.36

Answer: (a) Group B, (b) Group B, (c) SE ≈ 3.36.

✓ Answer checked by Claude Sonnet 5.5

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