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
To find the standard deviation of the given set of data, we first need to calculate the mean and then find the differences between each data point and the mean.
Data Points: 7.2, 8.9, 2.7, 11.6, 5.8, 10.2
1. Calculate the mean:
mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6
mean = 46.4 / 6
mean = 7.73
2. Find the differences between each data point and the mean:
7.2 - 7.73 = -0.53
8.9 - 7.73 = 1.17
2.7 - 7.73 = -5.03
11.6 - 7.73 = 3.87
5.8 - 7.73 = -1.93
10.2 - 7.73 = 2.47
3. Square each difference:
(-0.53)^2 = 0.2809
(1.17)^2 = 1.3689
(-5.03)^2 = 25.3009
(3.87)^2 = 14.9969
(-1.93)^2 = 3.7249
(2.47)^2 = 6.1009
4. Calculate the sum of squared differences:
0.2809 + 1.3689 + 25.3009 + 14.9969 + 3.7249 + 6.1009 = 51.7734
5. Calculate the variance:
variance = sum of squared differences / (n-1)
variance = 51.7734 / (6-1)
variance = 51.7734 / 5
variance = 10.35468
6. Calculate the standard deviation:
standard deviation = square root of variance
standard deviation = √10.35468
standard deviation ≈ 3.219
Therefore, the standard deviation of the given set of data is approximately 3.219.