The weights (in kilograms) of a group of ten randomly selected men are as follows:
79, 79, 94, 89, 91, 82, 86, 76, 83, 94
Calculate the mean and the standard deviation. Round to two decimal places, wherever applicable.
Mean:
Standard deviation:
Mean = (79 + 79 + 94 + 89 + 91 + 82 + 86 + 76 + 83 + 94) / 10
Mean = 857 / 10
Mean = 85.7 kg
Standard deviation = sqrt((Σ(x - mean)^2) / n)
Standard deviation = sqrt(((79-85.7)^2 + (79-85.7)^2 + ... + (94-85.7)^2) / 10)
Standard deviation = sqrt((42.49 + 42.49 + 68.89 + 12.01 + 29.16 + 10.89 + 7.29 + 94.09 + 1.69 + 68.89) / 10)
Standard deviation = sqrt(377.99 / 10)
Standard deviation ≈ sqrt(37.799)
Standard deviation ≈ 6.15 kg
Therefore, the mean weight of the group of ten men is 85.7 kg and the standard deviation is approximately 6.15 kg.