The standard deviation for the given data set is approximately 2.12.
Let's calculate the standard deviation for the given data set:
Data set: 9, 4, 6, 5, 4, 5, 5, 10
Find the mean.
Mean = (9 + 4 + 6 + 5 + 4 + 5 + 5 + 10) / 8
Mean = 48 / 8
Mean = 6
Find the difference between each number and the mean.
(9 - 6) = 3
(4 - 6) = -2
(6 - 6) = 0
(5 - 6) = -1
(4 - 6) = -2
(5 - 6) = -1
(5 - 6) = -1
(10 - 6) = 4
Square each result.
3^2 = 9
(-2)^2 = 4
0^2 = 0
(-1)^2 = 1
(-2)^2 = 4
(-1)^2 = 1
(-1)^2 = 1
4^2 = 16
Find the mean of those squared differences.
Mean of squared differences = (9 + 4 + 0 + 1 + 4 + 1 + 1 + 16) / 8
Mean of squared differences = 36 / 8
Mean of squared differences = 4.5
Take the square root of the mean of squared differences.
Standard deviation = √4.5
Standard deviation ≈ 2.12 (rounded to two decimal places)
Therefore, the standard deviation for the given data set is approximately 2.12.
Question
How do you find the standard deviation for the population 9, 4, 6, 5, 4, 5, 5, 10?