Question

Use the destribution below and determine the range,variance,and standard deviation of the population function
V=1-2-3-4-6-0
F=1-2-3-4-3-2

Answer 1

The range is the difference between the maximum and minimum values of the distribution. Therefore, the range of V is:

Range(V) = 6 - (-3) = 9

The variance is a measure of how spread out the values of the distribution are. It can be calculated as the sum of the squared deviations from the mean, divided by the number of observations. However, we need to calculate the mean of the distribution first:

Mean(V) = (1 + 2 + 3 + 4 + 6 + 0) / 6 = 2.33

Now we can calculate the variance of V:

Variance(V) = [(1 - 2.33)^2 + (2 - 2.33)^2 + (3 - 2.33)^2 + (4 - 2.33)^2 + (6 - 2.33)^2 + (0 - 2.33)^2] / 6
= 6.29

The standard deviation is the square root of the variance, and it represents the typical distance between the values of the distribution and the mean:

Standard deviation(V) = sqrt(Variance(V)) = sqrt(6.29) = 2.51

Using the same method, we can calculate the range, variance, and standard deviation of F:

Range(F) = 4 - 1 = 3

Mean(F) = (1 + 2 + 3 + 4 + 3 + 2) / 6 = 2.5

Variance(F) = [(1 - 2.5)^2 + (2 - 2.5)^2 + (3 - 2.5)^2 + (4 - 2.5)^2 + (3 - 2.5)^2 + (2 - 2.5)^2] / 6
= 0.83

Standard deviation(F) = sqrt(Variance(F)) = sqrt(0.83) = 0.91