Question 199781: Find the five-number summary of the following set of numbers.
0.16, 0.08, 0.27, 0.20, 0.22, 0.32, 0.25, 0.18, 0.28, 0.27
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! From Wikipedia, the five-number summary of a set of values consists of:
1. the sample minimum (smallest observation)
2. the lower quartile or first quartile (which cuts off the lowest 25% of the data)
3. the median (middle value)
4. the upper quartile or third quartile (which cuts off the highest 25% of the data)
5. the sample maximum (largest observation)
First sort the numbers into ascending order (from least to greatest):
0.08,0.16,0.18,0.20,0.22,0.25,0.27,0.27,0.28,0.32
Now let's find the 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.
0.08, 0.16, 0.18, 0.20,  ,  , 0.27, 0.27, 0.28, 0.32
Since the middle is in between the numbers 0.22 and 0.25, add them up and divide that sum by 2.
So the median is 0.235
Now let's break up the data set into two halves:
Set #1: 0.08,0.16,0.18,0.20,0.22
Set #2: 0.25,0.27,0.27,0.28,0.32
Now use the same technique to find the median to find the medians of the two data sets above to get the medians 0.18 and 0.27. So the first quartile is 0.18 and the third quartile is 0.27.
Finally, take note that the smallest value of the original data set is 0.08 and the largest is 0.32. So the min is 0.08 and the max is 0.32
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Summary:
1) Min = 0.08
2) 1st Quartile = 0.18
3) Median = 0.235
4) 3rd Quartile = 0.27
4) Max = 0.32
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