Question 712177: Calculate the mean, the median, and the mode for each of the following data sets:
(Also find standard deviation)
a. 82,80,63,75,92,80,92,90,80,80
b. 5,5,5,5,5,10
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do part a) and let you do part b)
First sort the numbers into ascending order (from least to greatest):
63,75,80,80,80,80,82,90,92,92
Sample Mean:
To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 10).
So the mean is 81.4
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Median:
To find the median, count off about 5 spaces (just take half of the size of the list, which is 10) from the beginning of the list until you hit the middle. Now count count off about 5 spaces from the end of the list until you hit the middle.
63, 75, 80, 80,  , , 82, 90, 92, 92
Since the middle is in between the numbers 80 and 80, add them up and divide that sum by 2.
So the median is 80
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Mode:
To find the mode, simply look for any repeating numbers. If there is one number that occurs more frequently than any other number, then that number is the mode.
Since 80 repeats itself 4 times (which is more frequent than any other number), the mode is 80
So the mode is 80
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Sample Standard Deviation (i.e. take a random sample of population and not measure whole population):
Use this formula to find the Sample standard deviation:
Sample Standard Deviation:^2}) where  is the average,  is the ith number, and  is the number of numbers
So we can replace N with 10
^2})
Subtract  to get 9
^2})
Replace with 81.4
^2})
Expand the summation (replace each  with the respective number)
Subtract the terms in the parenthesis
Square each term
Add up all of the terms
Multiply
Take the square root
So the sample standard deviation is
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