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AP Statistics : How to find the percentiles for a data set

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Example Question #1 : Statistical Concepts

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 : How To Find The Percentiles For A Data Set

The following data set represents Mr. Marigold's students' scores on the final. If you got a 90 on the final, what percentile does that place you in?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Possible Answers:

$\small 88th$ percentile

$\small 12th$ percentile

$\small 84th$ percentile

$\small 16th$ percentile

Correct answer:

$\small 88th$ percentile

Explanation:

Your percentile is the percent of the data set that is at your score or below.

There are 26 students in this particular class.

Of those students, 23 students were at a 90 or below.

$\small \frac{23}{26} \approx 0.88$ , or $\small 88 \%$ .

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

The following data set represents Mr. Marigold's students' scores on the final. If you are in the 46th percentile, what did you score?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Possible Answers:

$\small 85$

$\small 66$

$\small 81$

Correct answer:

Explanation:

If you scored in the 46th percentile, that means that 46% of your classmates scored the same as or worse than you.

This class has 26 students, and 46% of 26 is about 12.

Starting at 66 and counting 12 students forward would give you a 78.

This means that if you scored a 78, 12 students either had the same score or worse, so that is the 46th percentile.

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Example Question #2 : How To Find The Percentiles For A Data Set

The following data set represents Mr. Marigold's students' scores on the final. If you are in the 96th percentile, what did you score?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Possible Answers:

$\small 92$

$\small 96$

$\small 77.5$

$\small 69$

Correct answer:

$\small 92$

Explanation:

If you scored in the 96th percentile, that means that 96% of your classmates scored the same as or worse than you.

This class has 26 students, and 96% of 26 is about 25.

If 25 of your classmates did the same as or worse than you, that means only one person did better than you - nice work.

You must have gotten a 92, because it's the second-best score.

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

The following data set represents Mr. Marigold's students' scores on the final. If you got a 74 on the final, what percentile does that place you in?

$\small \small \small 66, 69, 71, 71, 72, 73.5, 74, 74, 76.5, 76.5, 77.5, 78, 81$
$\small 81, 85, 86, 86, 86, 87, 87.5, 88.5, 89, 90, 92, 92, 100$

Possible Answers:

$\small 69th$ percentile

$\small 74th$ percentile

$\small 37th$ percentile

$\small 31st$ percentile

Correct answer:

$\small 31st$ percentile

Explanation:

If you scored a 74, you can count and discover that eight students did worse than or the same as you.

There are a total of 26 students in the class, so 8 students would be

$\small \frac{8}{26} \approx 0.307$ or around $\small 31 \%$ .

This places you in the 31st percentile.

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Example Question #2 : How To Find The Percentiles For A Data Set

Your class' scores on a recent quiz was listed on the board.

55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83

Calculate the $85^{th}$ percentile.

Possible Answers:

Correct answer:

Explanation:

To find the $n^{th}$ percentile, we find the product of 0.n and the number of items in the set.

p=0.n*k

We then round that number up if it is not a whole number, and the $p^{th}$ term in the set is the $n^{th}$ percentile.

For this problem, to find the $85^{th}$ percentile, we find that there are 20 items in the set. We find the product to be

p=0.85*20=17

Since p=17,

in order to find the $85^{th}$ percentile we find the $17^{th}$ term in the set, which is

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

Your gym class' shot put distances are listed in the set below.

14.67, 14.93, 15.2, 15.32, 15.47, 16.83, 16.92, 17.31, 18.92

Which score is the $95^{th}$ percentile?

Possible Answers:

18.92

17.31

14.67

16.92

Correct answer:

18.92

Explanation:

To find the $n^{th}$ percentile, we find the product of 0.n and the number of items in the set.

p=0.n*k

We then round that number up if it is not a whole number, and the $p^{th}$ term in the set is the $n^{th}$ percentile.

For this problem, to find the $95^{th}$ percentile, we find that there are items in the set. We find the product to be

$p=0.95*9=8.55\approx9$

Since p=9,

in order to find the $95^{th}$ percentile we find the $9^{th}$ term in the set, which is

18.92

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AP Statistics : How to find the percentiles for a data set

Study concepts, example questions & explanations for AP Statistics

All AP Statistics Resources

Example Questions

Example Question #1 : Statistical Concepts

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

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

Example Question #2 : How To Find The Percentiles For A Data Set

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

Example Question #2 : How To Find The Percentiles For A Data Set

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

All AP Statistics Resources

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