SOLUTION: : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, and 29.4 .Calculate the standard deviation of the time it took for the 8 participants to solve the puzzle. With complete or step by s

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Question 1181823: : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, and 29.4
.Calculate the standard deviation of the time it took for the 8
participants to solve the puzzle. With complete or step by step solution.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Compute the mean by adding up the values, and dividing by n = 8, since there are 8 items in this list.

xbar = sample mean
xbar = (sum of values)/n
xbar = (15.2+18.8+19.3+19.7+20.2+21.8+22.1+29.4)/8
xbar = (166.5)/8
xbar = 20.8125

Then subtract the xbar value from each x value in the list. Square the difference. This forms the column (x-xbar)^2 as shown below
x(x-xbar)^2
15.231.50015625
18.84.05015625
19.32.28765625
19.71.23765625
20.20.37515625
21.80.97515625
22.11.65765625
29.473.74515625
Adding up everything in that second column gives us 115.82875

Divide that by n-1 = 8-1 = 7
115.82875/7 = 16.5469642857142
This is the approximate value of the sample variance

Apply the square root to get
sqrt(16.5469642857142) = 4.06779599853708
This rounds to 4.07
The sample standard deviation is roughly 4.07

Answer: 4.07 approximately
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