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