# AP Statistics : Univariate Data

## Example Questions

### 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?

percentile

percentile

percentile

percentile

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.

, or .

### 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?

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.

### Example Question #3 : 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?

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.

### Example Question #31 : Univariate Data

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?

percentile

percentile

percentile

percentile

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

or around .

This places you in the 31st percentile.

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

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

Calculate the  percentile.

Explanation:

To find the  percentile, we find the product of  and the number of items  in the set.

We then round that number  up if it is not a whole number, and the  term in the set is the  percentile.

For this problem, to find the  percentile, we find that there are 20 items in the set. We find the product to be

Since

in order to find the  percentile we find the  term in the set, which is

### Example Question #6 : How To Find The Percentiles For A Data Set

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

Which score is the  percentile?

Explanation:

To find the  percentile, we find the product of  and the number of items  in the set.

We then round that number  up if it is not a whole number, and the  term in the set is the  percentile.

For this problem, to find the  percentile, we find that there are  items in the set. We find the product to be

Since

in order to find the  percentile we find the  term in the set, which is

### Example Question #1 : How To Use Boxplots To Summarize A Data Set

Which of the following is true based on the box plot?

i. The mean is .

ii. The range is approximately .

iii. The IQR is approximatly .

iii only

i,ii, and iii

ii only

ii and iii

i and ii

iii only

Explanation:

The median, not the mean is . The IQR is about . The range is about .

### Example Question #1 : Using Box And Whisker Plots

The horizontal line in the box of the box and whisker plot represents _____________.

Mode

Mean

Interquartile range

Median

Range

Median

Explanation:

A box and whisker plot separates the data into quartiles so that each quartile has an equal number of data points. The box indicates the interquartile range, that is, the top line of the box is the third quartile and the bottom line of the box is the second quartile. The line separating the second and third quartiles indicates the median. The lines outside of the box indicate the outer-quartiles (first and fourth).

### Example Question #241 : Ap Statistics

A distribution has a minimum of , a first quartile of , a median of , a third quartile of  and a maximum of . Which of the following are true?

1. The interquartile range is .
2. The distribution is skewed left.
3. The range is .

1 only

1 and 2

1 and 3

1, 2 and 3

2 and 3

1 and 3

Explanation:

1) and 3) come easily because of straightforward calculations - it's 2 that's the tough part.

1) is true because the interquartile range is defined as the third quartile minus the first quartile.

3) is true because the range of a data set is the difference of the maximum value and the minimum value.

Notice that the median is closer to the first quartile, indicating that the distribution is skewed right. (If the median were closer to the third quartile, that would indicate a distribution that is skewed left.) It can help to draw the boxplot of the data set in order to visualize it.

### Example Question #1 : How To Use Boxplots To Summarize A Data Set

Which data set could be represented by the following boxplot?

Explanation:

This boxplot is representing a data set with a median of 11. The data set

has a median of 13, so we can eliminate this choice. And while the data set does have a mean of 11, its median is 10.

To determine which of the remaining choices matches the boxplot, find the first and third quartiles. To find the first quartile, find the median of the lower half, excluding the median, in each case 11.

has a first quartile of 8

has a first quartile of 6

The boxplot shown has the lower end of the rectangle at 6, so the last data set listed is the correct answer.