SOLUTION: find the standard deviation of 75 77 78 78 79 80 80 81 84 85 87 89 90 91 HELP

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Question 117072: find the standard deviation of
75 77 78 78 79 80 80 81 84 85 87 89 90 91

HELP
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
First sort the numbers into ascending order (from least to greatest):
75,77,78,78,79,80,80,81,84,85,87,89,90,91

Now we need the mean. So add up all of the numbers and divide the sum by the number of numbers (which in this case is 14).
Mean=%2875%2B77%2B78%2B78%2B79%2B80%2B80%2B81%2B84%2B85%2B87%2B89%2B90%2B91%29%2F14=1154%2F14=82.4285714285714

So the mean is 82.4285714285714




Now that we have the mean, we can use this formula to find the standard deviation:

Standard Deviation: where is the arithmetic mean, is the ith number, and is the number of numbers

So we can replace N with 14



Replace with 82.4285714285714



Expand the summation (replace each x%5Bi%5D with the respective number)


sqrt%28%281%2F14%29%28%2875-82.4285714285714%29%5E2%2B%2877-82.4285714285714%29%5E2%2B%2878-82.4285714285714%29%5E2%2B%2878-82.4285714285714%29%5E2%2B%2879-82.4285714285714%29%5E2%2B%2880-82.4285714285714%29%5E2%2B%2880-82.4285714285714%29%5E2%2B%2881-82.4285714285714%29%5E2%2B%2884-82.4285714285714%29%5E2%2B%2885-82.4285714285714%29%5E2%2B%2887-82.4285714285714%29%5E2%2B%2889-82.4285714285714%29%5E2%2B%2890-82.4285714285714%29%5E2%2B%2891-82.4285714285714%29%5E2%29%29

Subtract the terms in the parenthesis

sqrt%28%281%2F14%29%28%28-7.429%29%5E2%2B%28-5.429%29%5E2%2B%28-4.429%29%5E2%2B%28-4.429%29%5E2%2B%28-3.429%29%5E2%2B%28-2.429%29%5E2%2B%28-2.429%29%5E2%2B%28-1.429%29%5E2%2B%281.571%29%5E2%2B%282.571%29%5E2%2B%284.571%29%5E2%2B%286.571%29%5E2%2B%287.571%29%5E2%2B%288.571%29%5E2%29%29

Square each term

sqrt%28%281%2F14%29%2855.190041%2B29.474041%2B19.616041%2B19.616041%2B11.758041%2B5.900041%2B5.900041%2B2.042041%2B2.468041%2B6.610041%2B20.894041%2B43.178041%2B57.320041%2B73.462041%29%29

Add up all of the terms

sqrt%28%281%2F14%29353.428574%29

Multiply

sqrt%2825.2448981428571%29

Take the square root

5.02443013115489

So the standard deviation is 5.02443013115489

Here is an online standard deviation calculator that will check your work.