Understanding Quartiles and Percentiles - Math

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Question

What is the probability of getting a sum of when rolling two six-sided fair dice?

Answer

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

Ways to get what you want:

So there are ways to get a .

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

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Question

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?

Answer

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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Question

$Q_{2}$ 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:

Answer

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

$Q_{2}=36$ 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

Compare your answer with the correct one above

Question

What is the probability of getting a sum of when rolling two six-sided fair dice?

Answer

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

Ways to get what you want:

So there are ways to get a .

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

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

$Q_{2}$ 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:

Answer

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

$Q_{2}=36$ 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

Compare your answer with the correct one above

Question

What is the probability of getting a sum of when rolling two six-sided fair dice?

Answer

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

Ways to get what you want:

So there are ways to get a .

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

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

$Q_{2}$ 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:

Answer

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

$Q_{2}=36$ 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

Compare your answer with the correct one above

Question

What is the probability of getting a sum of when rolling two six-sided fair dice?

Answer

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

Ways to get what you want:

So there are ways to get a .

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

Compare your answer with the correct one above

Question

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?

Answer

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.

Compare your answer with the correct one above

Question

$Q_{2}$ 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:

Answer

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

$Q_{2}=36$ 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

Compare your answer with the correct one above

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