SOLUTION: Can you please help me with this statistics question. I looked at the answer to question 84214, but was still not sure where to start. This question is from Algebra II, A Beka Book

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Question 86018: Can you please help me with this statistics question. I looked at the answer to question 84214, but was still not sure where to start. This question is from Algebra II, A Beka Book.
Keith's long jump distances in feet from the last 3 track meets: 23.8, 23.0, 22.6, 24.2, 23.8, 22.5, 23.1, 24.0.
How do you find the
a)mean, b) median, c) mode, d)range, e) standard deviation.
Thank you so much for your help.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
First sort the numbers into ascending order (from least to greatest):
22.5, 22.6, 23.0, 23.1,23.8, 23.8, 24.0, 24.2

a)
To find the mean, add up all of the numbers and divide the sum by the number of numbers (which in this case is 8).


b)
To find the median, count off 4 spaces until you hit the middle number. Since the middle is in between 2 numbers, add them up and divide that sum by 2.



c)
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 23.8 repeats itself 2 times, the mode is 23.8


d)
To find the range, subtract the largest number (in this case 24.2) and the smallest number (in this case 22.5) like this:





e)
Use this formula to find the standard deviation:


where is the average, is the ith number, and is the number of numbers

So we can replace N with 8



Replace with 23.375



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 standard deviation is
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