Question

What is the frequency distribution 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 frequency distribution shows that the population function has a range of 6, meaning that the values range from 0 to 6.

To find the variance of the population function, we need to find the mean of the values, which is:

(1+2+3+4+6+0)/6 = 2.67

Then we subtract the mean from each value, square the result, and multiply by its frequency:

(1-2.67)^2 * 1 = 2.11
(2-2.67)^2 * 2 = 1.78
(3-2.67)^2 * 3 = 0.30
(4-2.67)^2 * 1 = 1.11
(6-2.67)^2 * 1 = 9.16
(0-2.67)^2 * 2 = 7.12

Adding these values together gives us:

2.11 + 1.78 + 0.30 + 1.11 + 9.16 + 7.12 = 21.58

To find the variance, we divide this sum by the total frequency (10 in this case):

21.58/10 = 2.16

The standard deviation is the square root of the variance, so:

√2.16 = 1.47

Therefore, the range of the population function is 6, the variance is 2.16, and the standard deviation is 1.47.