Exploring One-Variable Data: AP Statistics Math Worksheet – PDF Download

AP Statistics One Variable Worksheet: problems 1–5

Problem 1: Classify variables

Classify each variable as categorical or quantitative.

1. The eye color of each student in a class.
2. The minutes of homework Priya did last night.
3. The area code of each phone number in a contact list.
4. The number of pets in Diego’s household.

Problem 2: Relative frequencies

A survey of 50 students asked which pet they own: dog 21, cat 15, fish 6, bird 3, and none 5. Find the relative frequency of each answer as a percent.

Problem 3: Reading a bar chart

The bar chart shows how 300 students get to school.

1. What percent of the students ride the bus?
2. What percent neither ride the bus nor take a car?

Problem 4: Mean and median

Jamal scored 12, 18, 9, 22, 15, 18 and 25 points in seven games. Find the mean and the median.

Problem 5: Effect of an outlier

A set of five delivery times (minutes) is 14, 16, 17, 19 and 20. A sixth delivery takes 80 minutes. Find the mean and median before and after the 80 is added, and say which statistic is resistant.

AP Statistics One Variable Worksheet: problems 6–10

Problem 6: Range and IQR

Find the range and the IQR of these 11 ordered values: 4, 7, 9, 10, 12, 13, 15, 18, 19, 22, 30.

Problem 7: Five-number summary

Mei counted the text messages she sent on 12 days: 8, 12, 15, 15, 18, 22, 25, 27, 31, 34, 40, 52. Find the five-number summary and decide whether any value is an outlier by the 1.5 IQR rule.

Problem 8: Sample standard deviation

Find the sample standard deviation \(s\) of 6, 9, 10, 13 and 17, to the nearest hundredth.

Problem 9: Shape and median from a histogram

The histogram shows nightly homework time for 40 students.

1. Describe the shape.
2. In which class does the median lie?
3. Is the mean likely to be greater than, less than, or about equal to the median? Explain.

Problem 10: Counting from a histogram

The histogram shows the quiz scores of 30 students.

1. How many students scored below 70?
2. What percent of the students scored 80 or higher?
3. Which class contains the median?

AP Statistics One Variable Worksheet: problems 11–15

Problem 11: Test for outliers with IQR

Ethan recorded the minutes he spent on 10 bus rides: 22, 24, 25, 27, 28, 29, 31, 33, 34, 62. Use the 1.5 IQR rule to decide whether 62 is an outlier.

Problem 12: Reading a boxplot

The boxplot shows daily steps, in thousands, recorded by Sofia.

1. State the median, Q1 and Q3.
2. Find the IQR and check with the 1.5 IQR rule that 17 is an outlier.
3. About what percent of the days had between 5 and 9 thousand steps?

Problem 13: Compute a z-score

Scores on a history exam have mean 72 and standard deviation 6.

1. Find the z-score of a student who scored 84.
2. A student has a z-score of \(-1.5\). What was the score?

Problem 14: Compare two z-scores

Jamal scored 78 on a math exam with mean 70 and standard deviation 5. Sofia scored 85 on a science exam with mean 75 and standard deviation 8. Who did better relative to the class? Justify with z-scores.

Problem 15: Percentiles

A class of 25 students took an exam, and Ethan scored higher than 21 of them. Another class has 40 students, and Maya is at the 60th percentile there.

1. Find Ethan’s percentile.
2. How many students scored below Maya?

AP Statistics One Variable Worksheet: problems 16–20

Problem 16: Empirical rule percentages

The lengths of the fish in a lake are approximately normal with mean 14 inches and standard deviation 2 inches.

1. About what percent of the fish are between 12 and 18 inches long?
2. About what percent are longer than 18 inches?

Problem 17: Normal probability above a value

A pizza shop’s delivery times are approximately normal with mean 12.0 minutes and standard deviation 2.5 minutes. Find the percent of deliveries that take more than 15 minutes.

Problem 18: Value at a percentile

State exam scores are approximately normal with mean 500 and standard deviation 100. Find the score at the 90th percentile, to the nearest whole number.

Problem 19: Compare two distributions

Fifteen students in each of two groups timed a jigsaw puzzle. The boxplots summarize the times .

Compare the two distributions in context, addressing center, spread and shape.

Problem 20: Two outlier rules

A Little League team scored 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9 and 20 runs in 12 games. Apply (a) the 1.5 IQR rule and (b) the rule using 2 standard deviations from the mean. Which values, if any, are outliers under each rule?

AP Statistics One Variable Worksheet: problems 21–22

Problem 21: Changing units

The daily high temperatures in a city one July had mean 20 °C, median 19 °C, standard deviation 4 °C and IQR 6 °C. Find each of the four statistics in degrees Fahrenheit using \(F=1.8C+32\).

Problem 22: Salaries at a bakery

A bakery pays its nine employees (in dollars per year) 31,000; 33,500; 34,000; 35,000; 36,500; 38,000; 39,000; 41,000 and 180,000 (the owner).

1. Find the mean and median salary.
2. Use the 1.5 IQR rule to decide whether the owner’s salary is an outlier.
3. Which measure of center better describes a typical employee’s pay? Explain.

How to use this ap statistics one variable worksheet

Print this ap statistics one variable worksheet as a PDF, solve every problem on paper, then compare with the answer key.

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