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High School Math : Understanding Quartiles and Percentiles

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Example Question #1 : How To Find The Percentiles For A Data Set

The 70th and 80th percentiles of a set of scores are 78 and 86, respectively; the interquartile range of the scores is 41. Which of these scores is more likely than the others to be at the 25th percentile?

Possible Answers:

Correct answer:

Explanation:

The interquartile range of a set of scores is the difference between the third and first quartile - that is, the difference between the 75th and 25th percentiles. The 75th percentile is between 78 and 86, so, if 41 is subtracted from those numbers, the upper and lower bounds of the 25th percentile can be found.

$P_{70} < P_{75} < P_{80}$

$P_{70}- IR < P_{75} - IR < P_{80}- IR$

$P_{70}- IR < P_{25} < P_{80}- IR$

$78- 41 < P_{25} < 86- 41$

$37 < P_{25} < 45$

Of our choices, only 40 falls in this range.

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Example Question #1 : Understanding Quartiles And Percentiles

What is the probability of getting a sum of $5,\; 6,\; or\; 7$ when rolling two six-sided fair dice?

Possible Answers:

$\frac{7}{12}$

$\frac{5}{9}$

$\frac{5}{12}$

$\frac{1}{2}$

$\frac{4}{9}$

Correct answer:

$\frac{5}{12}$

Explanation:

The sample space, or total possible outcomes, when rolling two six-sided dice is .

Ways to get what you want:

$5: 1,4\;\; \; 2,3\; \; \; 3,2\; \; \; 4,1$

$6: 1,5\; \; \; 2,4\; \; \; 3,3\; \; 4,2\; \; \; 5,1$

$7: 1,6\; \; \; 2,5\; \; \; 3,4\; \; \; 4,3\; \; \; 5,2\; \; \; 6,1$

So there are ways to get a $5,6,or\; 7$ .

So the probability becomes $\frac{15}{36}=\frac{5}{12}$

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Example Question #2 : Understanding Quartiles And Percentiles

$Q_{2}$ is the median of the overall data set. $Q_{1}$ is the median of the lower half of the data set. $Q_{3}$ is the median of the upper half of the data set.

Find the interquartile range $\left ( Q_{3}-Q_{1}\right)$ for the following data set:

$23,\; 45,\; 32,\; 29,\; 37,\; 47,\; 21,\; 36,\; 52$

Possible Answers:

Correct answer:

Explanation:

First, put the data set in order from smallest to largest:

$21,\; 23,\; 29,\; 32,\; 36,\; 37,\; 45,\; 47, \; 52$

$Q_{2}=36$ which is the middle number in the data set.

$Q_{1}= 26$ which is the average of the two middle numbers of the lower half of the data set.

$Q_{3}=46$ which is the average of the two middle numbers of the upper half of the data set.

Thus the interquartile range is $Q_{3}-Q_{1}=46-26=20$

Note, the range of the data set is given by the largest number minus the smallest number, or 52-21=31

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High School Math : Understanding Quartiles and Percentiles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Percentiles For A Data Set

Example Question #1 : Understanding Quartiles And Percentiles

Example Question #2 : Understanding Quartiles And Percentiles

All High School Math Resources

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