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¯¯¯¯ (X−X¯¯¯¯)2 7.2 8.9 2.7 11.6 5.8 10.2 (1 point) Responses 8.62 8.62 2.93 2.93 51.75 51.75 7.73
To find the standard deviation, we need to follow these steps:
1. Find the mean (X¯¯¯¯):
Sum of all numbers = 7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2 = 46.4
Mean (X¯¯¯¯) = Sum of all numbers / Total number of numbers
Mean (X¯¯¯¯) = 46.4 / 6
Mean (X¯¯¯¯) = 7.73
2. Find the difference between each number and the mean (X - X¯¯¯¯):
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. Find the square of the differences ((X - X¯¯¯¯)^2):
(-0.53)^2 = 0.28
(1.17)^2 = 1.37
(-5.03)^2 = 25.30
(3.87)^2 = 14.98
(-1.93)^2 = 3.73
(2.47)^2 = 6.10
4. Find the sum of all the squared differences:
0.28 + 1.37 + 25.30 + 14.98 + 3.73 + 6.10 = 51.76
5. Find the variance:
Variance = Sum of all squared differences / Total number of numbers
Variance = 51.76 / 6
Variance = 8.6267 (rounded to four decimal places)
6. Find the standard deviation:
Standard Deviation = Square root of Variance
Standard Deviation = Square root of 8.6267
Standard Deviation = 2.94 (rounded to two decimal places)