Find the starndard deviation to the nearest hundreths and then compare the variability of the datasets
Dataset A: 10, 8, 10, 8, 8, 5
Dataset B: 9, 10, 8, 10, 11, 6
To find the standard deviation of each dataset, we first need to find the mean of each dataset.
Dataset A:
Mean = (10 + 8 + 10 + 8 + 8 + 5) / 6 = 49 / 6 = 8.17
Calculate the squared differences from the mean for each value in Dataset A:
(10 - 8.17)^2 = 3.33
(8 - 8.17)^2 = 0.03
(10 - 8.17)^2 = 3.33
(8 - 8.17)^2 = 0.03
(8 - 8.17)^2 = 0.03
(5 - 8.17)^2 = 10.05
Calculate the variance:
Variance = (3.33 + 0.03 + 3.33 + 0.03 + 0.03 + 10.05) / 6 = 17.78 / 6 = 2.9633
Standard deviation of Dataset A = √2.9633 ≈ 1.72
Dataset B:
Mean = (9 + 10 + 8 + 10 + 11 + 6) / 6 = 54 / 6 = 9
Calculate the squared differences from the mean for each value in Dataset B:
(9 - 9)^2 = 0
(10 - 9)^2 = 1
(8 - 9)^2 = 1
(10 - 9)^2 = 1
(11 - 9)^2 = 4
(6 - 9)^2 = 9
Calculate the variance:
Variance = (0 + 1 + 1 + 1 + 4 + 9) / 6 = 16 / 6 = 2.67
Standard deviation of Dataset B = √2.67 ≈ 1.63
Comparing the two standard deviations, Dataset A has a slightly higher standard deviation (1.72) compared to Dataset B (1.63), indicating that Dataset A has slightly more variability in its values.