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
To calculate the standard deviation for each dataset, we first need to find the mean of each dataset:
Dataset A: Mean = (11+7+12+8+9+5)/6 = 8.67
Dataset B: Mean = (10+8+10+8+8+4)/6 = 8
Next, we calculate the squared differences between each data point and the mean for each dataset:
Dataset A:
(11-8.67)^2 = 5.4689
(7-8.67)^2 = 2.7889
(12-8.67)^2 = 11.4289
(8-8.67)^2 = 0.4489
(9-8.67)^2 = 0.1089
(5-8.67)^2 = 13.8489
Dataset B:
(10-8)^2 = 4
(8-8)^2 = 0
(10-8)^2 = 4
(8-8)^2 = 0
(8-8)^2 = 0
(4-8)^2 = 16
Now, we sum up the squared differences for each dataset and divide by the number of data points minus 1, then take the square root of that result:
Dataset A:
Sum = 5.4689 + 2.7889 + 11.4289 + 0.4489 + 0.1089 + 13.8489 = 34.0835
Variance = 34.0835 / (6-1) = 6.8167
Standard Deviation = sqrt(6.8167) ≈ 2.61
Dataset B:
Sum = 4 + 0 + 4 + 0 + 0 + 16 = 24
Variance = 24 / (6-1) = 4.8
Standard Deviation = sqrt(4.8) ≈ 2.19
Therefore, the standard deviation for Dataset A is approximately 2.61 and for Dataset B is approximately 2.19. This indicates that Dataset A has greater variability than Dataset B.