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Safari File Edit View History Bookmarks Window Help Review Question 5 (of 60 score This Question 5. 10.00 points. Scores on the final in a statistics class are as follows. 75 25 75 62 80 85 80 99 90 60 86 92 40 74 72 65 87 70 85 70 Click here for the Excel Data File a. Calculate the 25th, 50th, and 75th percentiles. (Do not round intermediate calculations. Round your answers to 2 decimal places.) 25th percentile 50th percentile 75th percentile b-1. Select a box plot. x Plot B Box Plot A of scores MacBook ProExplanation / Answer
a.
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
25 40 60 62 65 70 70 72 74 75 75 80 80 85 85 86 87 90 92 99
So, the bottom half is
25 40 60 62 65 70 70 72 74 75
The median of these numbers is 67.5.
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
25 40 60 62 65 70 70 72 74 75 75 80 80 85 85 86 87 90 92 99
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median=75+75/2=75
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.
25 40 60 62 65 70 70 72 74 75 75 80 80 85 85 86 87 90 92 99
So, the upper half is
75 80 80 85 85 86 87 90 92 99
The median of these numbers is 85.5.
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