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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¯¯¯¯
−
¯
(X−X¯¯¯¯)2
(
−
¯
)
2
7.2
8.9
2.7
11.6
5.8
10.2
(1 point)
Responses
51.75
51.75
8.62
8.62
7.73
7.73
2.93
To find the standard deviation, we first need to calculate the mean of the data set.
Mean (X bar) = sum of all values / number of values
Mean (X bar) = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6
Mean (X bar) = 46.4 / 6
Mean (X bar) = 7.73
Now, we need to calculate the squared differences between each value and the mean.
(X - X bar) = (7.2 - 7.73) = -0.53
(X - X bar) = (8.9 - 7.73) = 1.17
(X - X bar) = (2.7 - 7.73) = -5.03
(X - X bar) = (11.6 - 7.73) = 3.87
(X - X bar) = (5.8 - 7.73) = -1.93
(X - X bar) = (10.2 - 7.73) = 2.47
Next, we calculate the squared differences.
(-0.53)^2 = 0.2809
(1.17)^2 = 1.3689
(-5.03)^2 = 25.3009
(3.87)^2 = 14.9769
(-1.93)^2 = 3.7249
(2.47)^2 = 6.1009
Now, sum up all the squared differences.
0.2809 + 1.3689 + 25.3009 + 14.9769 + 3.7249 + 6.1009 = 51.7535
To find the sample standard deviation, divide the sum of squared differences by n-1 (6-1 = 5) and then take the square root.
Standard Deviation = sqrt(51.7535 / 5)
Standard Deviation = sqrt(10.3507)
Standard Deviation ≈ 3.22
Therefore, the standard deviation of the given data set is approximately 3.22.