Question

Find the​ mean, variance, and standard deviation for the data set.
7​, 13​, 10​, 4​, 12​, 7​, 11​, 7​, 17​, 12

Answers

GPT 3.5
To find the mean, add up all the numbers and divide by the total number of numbers:

Mean = (7 + 13 + 10 + 4 + 12 + 7 + 11 + 7 + 17 + 12) / 10 = 100 / 10 = 10

To find the variance, first find the differences between each number and the mean, square those differences, add them up, and then divide by the total number of numbers:

Variance = ((7 - 10)^2 + (13 - 10)^2 + (10 - 10)^2 + (4 - 10)^2 + (12 - 10)^2 + (7 - 10)^2 + (11 - 10)^2 + (7 - 10)^2 + (17 - 10)^2 + (12 - 10)^2) / 10
= (9 + 9 + 0 + 36 + 4 + 9 + 1 + 9 + 49 + 4) / 10
= 130 / 10
= 13

To find the standard deviation, take the square root of the variance:

Standard deviation = √13 ≈ 3.61

Therefore, the mean is 10, the variance is 13, and the standard deviation is approximately 3.61.