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Breaking strength: average, median, SD

Short answer

Material 1: mean 175.33 lb, median 176 lb, variance 363.47 lb², SD 19.06 lb. Material 2: mean 175.67 lb, median 182.5 lb, variance 471.47 lb², SD 21.71 lb. Material 3: mean 179.83 lb, median 177.5 lb, variance 223.77 lb², SD 14.96 lb.

The following are data on the breaking strength (in pounds) of 3 kinds of material:

Material 1144181200187169171
Material 2186194176182133183
Material 3197165180198175164
i) Calculate the average breaking strength and the median breaking strength for each material.
ii) Calculate standard deviation and variance for each material.

For each material n = 6. Mean = Σx/n, median is the average of the 3rd and 4th ordered values, sample variance s² = [Σx² − (Σx)²/n]/(n − 1), and s = √s².

i) Average and median

MaterialOrdered valuesΣxMeanMedian
1144, 169, 171, 181, 187, 2001052175.33(171 + 181)/2 = 176
2133, 176, 182, 183, 186, 1941054175.67(182 + 183)/2 = 182.5
3164, 165, 175, 180, 197, 1981079179.83(175 + 180)/2 = 177.5

ii) Variance and standard deviation

MaterialΣx²Sxxs² (÷ 5)s
1186,2681817.33363.4719.06
2187,5102357.33471.4721.71
3195,1591118.83223.7714.96

Working for Material 1:

Sxx = 186,268 − (1052)²/6 = 186,268 − 184,450.67 = 1817.33
s²  = 1817.33 / 5 = 363.47
s   = 19.06

Answer: averages 175.33, 175.67, 179.83 lb; medians 176, 182.5, 177.5 lb; variances 363.47, 471.47, 223.77 lb²; SDs 19.06, 21.71, 14.96 lb. Material 3 has the highest average and the smallest spread. Material 2 has the greatest spread.

✓ Answer checked by Claude Sonnet 5.5

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