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
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
To determine the range, variance, and standard deviation of a population, we need to first calculate some statistics based on the given data.
Range:
The range is the difference between the maximum and minimum values in a dataset.
In this case, the maximum value in the V distribution is 6, and the minimum value is -4. Therefore, the range is 6 - (-4) = 10.
Variance:
Variance measures the spread or dispersion of data values around the mean.
To calculate the variance, we follow these steps:
1. Calculate the mean: (1 + 2 + 3 + 4 + 6 + 0) / 6 = 16 / 6 = 2.67 (rounded to two decimal places).
2. Calculate the squared difference between each value and the mean:
(1 - 2.67)^2 = 2.8889
(2 - 2.67)^2 = 0.4489
(3 - 2.67)^2 = 0.1089
(4 - 2.67)^2 = 1.7689
(6 - 2.67)^2 = 11.5429
(0 - 2.67)^2 = 7.1289
3. Calculate the sum of the squared differences:
2.8889 + 0.4489 + 0.1089 + 1.7689 + 11.5429 + 7.1289 = 23.8774.
4. Divide the sum by the number of observations (in this case, 6):
23.8774 / 6 = 3.9796 (rounded to four decimal places).
Therefore, the variance in the V distribution is approximately 3.9796.
Standard Deviation:
The standard deviation is the square root of variance; it measures the average amount by which each value deviates from the mean.
To calculate the standard deviation, we take the square root of the variance:
√3.9796 ≈ 1.995 (rounded to three decimal places).
Therefore, the standard deviation in the V distribution is approximately 1.995.