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.
11,8,5,15,16,6,12,18,15,5
Range:
Range = max - min
Range = 18 - 5
Range = 13
Population Variance:
1. Calculate the mean:
Mean = (11 + 8 + 5 + 15 + 16 + 6 + 12 + 18 + 15 + 5) / 10
Mean = 101 / 10
Mean = 10.1
2. Calculate the squared differences:
(11 - 10.1)^2 = 0.81
(8 - 10.1)^2 = 4.41
(5 - 10.1)^2 = 25.01
(15 - 10.1)^2 = 24.01
(16 - 10.1)^2 = 34.81
(6 - 10.1)^2 = 16.81
(12 - 10.1)^2 = 3.61
(18 - 10.1)^2 = 62.41
(15 - 10.1)^2 = 24.01
(5 - 10.1)^2 = 25.01
3. Sum the squared differences:
Sum = 0.81 + 4.41 + 25.01 + 24.01 + 34.81 + 16.81 + 3.61 + 62.41 + 24.01 + 25.01
Sum = 220.49
4. Calculate the population variance:
Population Variance = Sum / N
Population Variance = 220.49 / 10
Population Variance = 22.049
Population Standard Deviation:
Population Standard Deviation = √population variance
Population Standard Deviation = √22.049
Population Standard Deviation ≈ 4.7
Therefore, the range is 13, population variance is 22.049, and the population standard deviation is approximately 4.7.