Be sure you are writing out your steps. You will have to submit your shown work for
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)
8.62
7.73
51.75
2.93
To find the standard deviation, we first need to calculate the mean of the data set.
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 46.4 / 6 = 7.73
Next, we calculate the squared difference between each data point and the mean:
(7.2 - 7.73)^2 = 0.27
(8.9 - 7.73)^2 = 1.36
(2.7 - 7.73)^2 = 25.0
(11.6 - 7.73)^2 = 14.88
(5.8 - 7.73)^2 = 3.37
(10.2 - 7.73)^2 = 6.05
Next, we find the sum of all the squared differences:
0.27 + 1.36 + 25.0 + 14.88 + 3.37 + 6.05 = 51.93
To get the variance, we divide the sum of squared differences by the number of data points:
Variance = 51.93 / 6 = 8.655
Finally, to get the standard deviation, we take the square root of the variance:
Standard Deviation = √8.655 = 2.94
Therefore, the standard deviation of the given data set is 2.94.