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AP Statistics : AP Statistics

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Example Questions

Example Question #231 : Ap Statistics

The standard deviation of a population is 7.5. What is the variance of the population?

Possible Answers:

2.74

54.5

56.25

46.25

Correct answer:

56.25

Explanation:

This question illustrates the close relationship between the concepts of variance and standard deviation. We can find variance even though we do not know the values in the population if we know the standard deviation. Simply square the standard deviation to find the variance.

$7.5^{2}=56.25$

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

Obtain a normal distribution table or calculator for this problem.

Approximate the $\small 90^{th}$ -percentile on the standard normal distribution.

Possible Answers:

$\small 1.65$

$\small 1.28$

$\small 1$

$\small 2$

Correct answer:

$\small 1.28$

Explanation:

The $\small 90^{th}$ -percentile is the value such that $\small 90$ percent of values are less than it.

Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate $\small 90^{th}$ -percentile is about $\small 1.28$ .

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Example Question #231 : Ap Statistics

Find the first and third quartile for the set of data

10,10,11,12,13,14,21,22,25,26,29,35,37,38

Possible Answers:

$Q_1=14,\, Q_3=25$

$Q_1=11,\, Q_3=26$

$Q_1=13,\, Q_3=35$

$Q_1=12,\, Q_3=29$

Correct answer:

$Q_1=12,\, Q_3=29$

Explanation:

In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.

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 $25^{th}$ and $75^{th}$ percentile, we first find that there are 14 items in the set. We find their respective products to be

$p_{25}=0.25*14=3.5\approx4$ and

$p_{75}=0.75*14=10.5\approx11$

As such, the $25^{th}$ and $75^{th}$ percentiles are the fourth and eleventh terms in the set, or

$Q_1=12,\, Q_3=29$

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Example Question #22 : Univariate Data

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:

$\small 16th$ percentile

$\small 12th$ percentile

$\small 88th$ percentile

$\small 84th$ 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

$\small 37th$ percentile

$\small 74th$ 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 #31 : Data

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:

14.67

17.31

18.92

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 : AP Statistics

Study concepts, example questions & explanations for AP Statistics

All AP Statistics Resources

Example Questions

Example Question #231 : Ap Statistics

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

Example Question #231 : Ap Statistics

Example Question #22 : Univariate Data

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 #31 : Data

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

All AP Statistics Resources

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