Range:
Range = Max value - Min value
Range = 20 - 8
Range = 12
Population Variance:
Step 1: Find the mean
Mean = (14 + 12 + 20 + 19 + 11 + 13 + 10 + 8 + 18 + 15) / 10
Mean = 140 / 10
Mean = 14
Step 2: Find the squared difference from the mean for each value
(14-14)^2 = 0
(12-14)^2 = 4
(20-14)^2 = 36
(19-14)^2 = 25
(11-14)^2 = 9
(13-14)^2 = 1
(10-14)^2 = 16
(8-14)^2 = 36
(18-14)^2 = 16
(15-14)^2 = 1
Step 3: Find the sum of squared differences
Sum = 0 + 4 + 36 + 25 + 9 + 1 + 16 + 36 + 16 + 1
Sum = 144
Step 4: Calculate variance
Variance = Sum / N
Variance = 144 / 10
Variance = 14.4
Population Standard Deviation:
Population Standard Deviation = √Variance
Population Standard Deviation = √14.4
Population Standard Deviation ≈ 3.8
Therefore, the Range is 12, the Population Variance is 14.4, and the Population Standard Deviation is approximately 3.8.
Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place
than the largest number of decimal places given in the data.
14, 12, 20, 19, 11, 13, 10, 8, 18, 15
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Range:
Population Variance:
Population Standard Deviation:
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