: 2.93
To find the standard deviation, we first need to find the mean of the data set.
Mean (X¯) = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 46.4 / 6 = 7.73
Next, we subtract the mean from each data point and square the result:
(7.2 - 7.73)^2 = 0.5329
(8.9 - 7.73)^2 = 1.3577
(2.7 - 7.73)^2 = 25.3489
(11.6 - 7.73)^2 = 14.9769
(5.8 - 7.73)^2 = 3.3689
(10.2 - 7.73)^2 = 5.9989
Now, we find the average of these squared differences:
(0.5329 + 1.3577 + 25.3489 + 14.9769 + 3.3689 + 5.9989) / 6 = 51.5839 / 6 = 8.62
Finally, we take the square root of this average to find the standard deviation:
Standard Deviation = sqrt(8.62) = 2.936
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¯¯¯¯
𝑋
−
𝑋
¯
(X−X¯¯¯¯)2
(
𝑋
−
𝑋
¯
)
2
7.2
8.9
2.7
11.6
5.8
10.2
Responses
51.75
51.75 - no response given
8.62
8.62 - no response given
7.73
7.73 - no response given
2.93
2.93 - correct
Score
1 answer