Question 874244: What is the median and range of the given data set?
10,25,40,35,15,5,20,30
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Sort out the data set:
5, 10, 15, 20, 25, 30, 35, 40
There are 8 values. This is an even number of values. So the median will be in between the two middle-most numbers (the median may or may not be in the list -- there are no guarantees).
More specifically, the median will be in between the elements at slot numbers 4 and 5 (divide 8 in half to get 4).
This means you can count 4 places over to get to the value of 20. The next number over is 25
The median will be the average of the two values 20 and 25. So average them to get (20 + 25)/2 = (45)/2 = 22.5
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Or you can do it this way
Step 1) Start with the list of numbers shown below
5, 10, 15, 20, 25, 30, 35, 40
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Step 2) Erase the outer pair of numbers (5 on the very left and 40 on the very right) to get the new list:
10, 15, 20, 25, 30, 35
Repeat this until the list reduces to exactly two values.
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Step 3) Erase the outer pair of numbers (10 on the very left and 35 on the very right) to get the new list:
15, 20, 25, 30
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Step 4) Erase the outer pair of numbers (15 on the very left and 30 on the very right) to get the new list:
20, 25
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We're left with exactly two numbers: 20 and 25. So we are done erasing values.
Average the two values to get (20 + 25)/2 = (45)/2 = 22.5
So the median is 22.5
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The range is equal to the difference in the largest value and smallest value
Range = Max - Min
Range = 40 - 5
Range = 35
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