A sample of eight math SAT scores is given below Find the fi

A sample of eight math SAT scores is given below:

Find the first and third quartiles and the interquartile range for this sample.

First Quartile =

Third Quartile =

Interquartile Range =

Solution

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A sample of eight math SAT scores is given below:
700 650 590 570 540 660 740 520

Find the first and third quartiles and the interquartile range for this sample

Answer

First rank data from lowest to highest:

520, 540, 570, 590, 650, 660, 700, 740

Then use the formula n*k/100, where n is the number of scores, k is 25 for the first quartile.

Since 8*25/100 = 2, the first quartile is the second score, which is 540.

To find the third quartile, since k would be 75, you would substitute 100-k for k in the formula and then count from largest to smallest:

So it would be 8*(100-75)/100 = 8*25/100 = 2, so the third quartile would be the second number from the highest, which is be 700.

The interquartile range is the difference between the first and third quartiles: 700-540 = 160.

So the answers are first quartile = 540, third quartile = 700, and interquartile distance = 160.