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

: 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