For the following set of data, find the sample standard deviation, to the nearest hundredth. 40, 86, 79, 25, 75, 67, 86, 38 40, 86, 79, 25, 75, 67, 86, 38
To find the sample standard deviation, we first need to find the mean of the data set.
Mean = (40 + 86 + 79 + 25 + 75 + 67 + 86 + 38) / 8
Mean = 556 / 8
Mean = 69.5
Next, we calculate the variance:
Variance = [ (40 - 69.5)^2 + (86 - 69.5)^2 + (79 - 69.5)^2 + (25 - 69.5)^2 + (75 - 69.5)^2 + (67 - 69.5)^2 + (86 - 69.5)^2 + (38 - 69.5)^2 ] / 7
Variance = [ 900.25 + 376.25 + 121.25 + 1806.25 + 34.25 + 6.25 + 376.25 + 979.25 ] / 7
Variance = 5604.0 / 7
Variance = 800.57
Finally, we calculate the sample standard deviation:
Sample Standard Deviation = sqrt(Variance)
Sample Standard Deviation = sqrt(800.57)
Sample Standard Deviation ≈ 28.29
Therefore, the sample standard deviation of the data set is approximately 28.29.