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each problem at the end
Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the
table and show the ending calculations in the following question to get full credit.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
X-X
X
X
2
(x-x)
7.2
8.9
2.7
11.6
5.8
10.2
(1 point)
The answers are:
8.62
7.73
51.75
2.93
To find the standard deviation, we first need to find the mean of the data set.
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6
Mean = 46.4 / 6
Mean = 7.73
Next, we need to find the squared differences between each data point and the mean.
(X - X)^2
(7.2 - 7.73)^2 = 0.2704
(8.9 - 7.73)^2 = 1.3657
(2.7 - 7.73)^2 = 25.4169
(11.6 - 7.73)^2 = 14.9857
(5.8 - 7.73)^2 = 3.3681
(10.2 - 7.73)^2 = 6.0817
Next, we find the sum of all the squared differences.
Sum = 0.2704 + 1.3657 + 25.4169 + 14.9857 + 3.3681 + 6.0817
Sum = 51.4885
To find the variance, we divide the sum of squared differences by the number of data points.
Variance = Sum / 6
Variance = 51.4885 / 6
Variance = 8.5814
Finally, the standard deviation is the square root of the variance.
Standard Deviation = √8.5814
Standard Deviation = 2.93
Therefore, the standard deviation of the given set of data is 2.93.