ACT Statistics Practice Questions with Answers

Mastering ACT statistics is essential for any student aiming for a competitive score, as data analysis and probability typically account for a significant portion of the math section. This guide provides comprehensive ACT Statistics Practice Questions with Answers to help you navigate concepts like mean, median, mode, range, and standard deviation with confidence.

Concept Explanation

ACT Statistics involves the collection, analysis, interpretation, and presentation of data sets to identify trends, central tendencies, and variability. At its core, the ACT tests your ability to calculate measures of central tendency—mean, median, and mode—and measures of spread, such as range and standard deviation. Understanding these concepts is a fundamental part of your ACT Prep journey.

The Mean (average) is calculated by summing all values in a set and dividing by the number of values. The Median is the middle value when the data is arranged in ascending order; if there is an even number of values, it is the average of the two middle numbers. The Mode is the value that appears most frequently. Beyond central tendency, the Range is the difference between the maximum and minimum values, while Standard Deviation measures how spread out the numbers are from the mean. For more advanced practice, you might find our AI Question Generator useful for creating custom data sets.

According to the ACT Official Site, statistics questions often require students to interpret charts, graphs, and tables. You may also encounter weighted averages and questions where you must determine how adding or removing a data point affects the mean or median. Visualizing data through box plots and histograms is another key skill evaluated on the exam.

Solved Examples

1. Finding the Missing Value: The average of five numbers is 18. Four of the numbers are 12, 15, 20, and 22. What is the fifth number?
   1. Use the mean formula: $\text{Average} = \frac{ \text{Sum}}{ \text{Count}}$.
   2. Set up the equation: $18 = \frac{12 + 15 + 20 + 22 + x}{5}$.
   3. Multiply both sides by 5: $90 = 69 + x$.
   4. Subtract 69 from 90: $x = 21$.
2. Changing the Mean: A student has an average of 84 on four exams. What score does the student need on the fifth exam to raise their average to 86?
   1. Calculate the current total points: $84 \times 4 = 336$.
   2. Calculate the required total points for five exams: $86 \times 5 = 430$.
   3. Subtract the current total from the required total: $430 - 336 = 94$.
   4. The student needs a 94.
3. Median of an Even Set: Find the median of the following set: {5, 12, 7, 18, 9, 21}.
   1. Arrange the numbers in ascending order: {5, 7, 9, 12, 18, 21}.
   2. Identify the two middle numbers: 9 and 12.
   3. Calculate the average of the middle numbers: $\frac{9 + 12}{2} = 10.5$.

Practice Questions

1. A set of data consists of the following integers: {4, 8, 15, 16, 23, 42}. What is the range of this data set?

2. The mean of a list of 7 numbers is 12. If one number is removed, the mean of the remaining 6 numbers becomes 11. What was the value of the number that was removed?

3. In a class of 20 students, the average score on a test was 75. In another class of 30 students, the average score on the same test was 85. What is the combined average score for all 50 students?

4. A data set has a mean of 50 and a standard deviation of 5. If every value in the data set is increased by 10, what will be the new mean and the new standard deviation?

5. The set {x, 7, 12, 15, 18} is ordered from least to greatest. If the median is 12 and the mean is 12, what is the value of x?

6. A bag contains 4 red marbles, 6 blue marbles, and 10 green marbles. If one marble is selected at random, what is the probability that it is NOT blue?

7. The frequency table below shows the number of goals scored by a soccer team in 10 games. What is the mode of the goals scored?

Goals	Frequency
0	2
1	4
2	3
3	1

8. If the variance of a data set is 49, what is the standard deviation?

9. A set of 5 numbers has a mean of 20. If a 6th number, 32, is added to the set, what is the new mean?

10. What is the median of the following set of numbers: {45, 12, 33, 27, 12, 50, 41}?

Answers & Explanations

1. Answer: 38. The range is the maximum minus the minimum. $42 - 4 = 38$.
2. Answer: 18. Total sum of 7 numbers = $7 \times 12 = 84$. Total sum of 6 numbers = $6 \times 11 = 66$. The removed number is $84 - 66 = 18$.
3. Answer: 81. Total points for Class 1: $20 \times 75 = 1,500$. Total points for Class 2: $30 \times 85 = 2,550$. Combined total: $4,050$. Combined average: $\frac{4,050}{50} = 81$.
4. Answer: Mean = 60, Standard Deviation = 5. Adding a constant to every value increases the mean by that constant but does not change the spread (standard deviation). For more on distribution, check our pharmacokinetics calculation examples which often use similar statistical distributions.
5. Answer: 8. The mean is 12, and there are 5 numbers. Total sum = $12 \times 5 = 60$. Sum of knowns: $7 + 12 + 15 + 18 = 52$. Therefore, $x = 60 - 52 = 8$.
6. Answer: 7/10 (or 0.7). Total marbles = $4 + 6 + 10 = 20$. Marbles that are not blue = $4 ( \text{red}) + 10 ( \text{green}) = 14$. Probability = $\frac{14}{20} = \frac{7}{10}$.
7. Answer: 1. The mode is the value with the highest frequency. The frequency of 1 goal is 4, which is the highest in the table.
8. Answer: 7. The standard deviation is the square root of the variance. $\sqrt{49} = 7$.
9. Answer: 22. Initial total = $5 \times 20 = 100$. New total = $100 + 32 = 132$. New mean = $\frac{132}{6} = 22$.
10. Answer: 33. Ordered set: {12, 12, 27, 33, 41, 45, 50}. The middle (4th) value is 33.

1. If the mean of five numbers is 10, what is the sum of the five numbers?

• A2
• B10
• C50
• D100

Frequently Asked Questions

What is the difference between mean and median on the ACT?

The mean is the calculated average of all numbers in a set, while the median is the specific middle value when the set is ordered. The ACT often asks how adding an outlier changes the mean significantly while the median remains relatively stable.

How do you calculate a weighted average?

To calculate a weighted average, multiply each value by its corresponding weight or frequency, sum those products, and divide by the total number of items. This is common in ACT questions involving class grades or mixture problems.

Does the ACT require you to calculate standard deviation by hand?

No, the ACT rarely requires the full manual calculation of standard deviation. Instead, you need to understand the concept—that a higher standard deviation indicates data is more spread out from the mean.

What is the range of a data set?

The range is the simplest measure of spread, calculated by subtracting the smallest value in a data set from the largest value. It provides a quick look at the total span of the data points.

How do I find the median if there is an even number of data points?

When a data set has an even number of values, the median is found by taking the arithmetic mean of the two middle numbers. You must first ensure the list is sorted in ascending or descending order.