Use the standard deviation to compare the variability of the datasets. Round to the nearest hundredths.
Dataset A: 11, 7, 12, 8, 9, 5
Dataset B: 10, 8,10,8,8,4
First, we need to calculate the standard deviation for each dataset.
For Dataset A:
Mean = (11 + 7 + 12 + 8 + 9 + 5) / 6 = 8.67
Squaring the differences from the mean:
(11-8.67)^2 = 4.83
(7-8.67)^2 = 2.79
(12-8.67)^2 = 11.31
(8-8.67)^2 = 0.45
(9-8.67)^2 = 0.11
(5-8.67)^2 = 13.69
Sum of squared differences = 4.83 + 2.79 + 11.31 + 0.45 + 0.11 + 13.69 = 33.18
Variance = 33.18 / 6 = 5.53
Standard deviation = √5.53 ≈ 2.35
For Dataset B:
Mean = (10 + 8 + 10 + 8 + 8 + 4) / 6 = 8
Squaring the differences from the mean:
(10-8)^2 = 4
(8-8)^2 = 0
(10-8)^2 = 4
(8-8)^2 = 0
(8-8)^2 = 0
(4-8)^2 = 16
Sum of squared differences = 4 + 0 + 4 + 0 + 0 + 16 = 24
Variance = 24 / 6 = 4
Standard deviation = √4 = 2
Therefore, Dataset A has a standard deviation of approximately 2.35 and Dataset B has a standard deviation of 2. By comparing the standard deviations, we can see that Dataset A has slightly higher variability compared to Dataset B.