Easy ACT Statistics Interpretation Practice Questions

Concept Explanation

Statistics interpretation on the ACT involves analyzing data sets to find central tendencies, identify distribution patterns, and make logical inferences from numerical information. At the easy level, this primarily focuses on the "Big Three" of statistics: mean, median, and mode, along with the range of a data set. The mean is the numerical average, calculated by summing all values and dividing by the count of values. The median is the middle value when the data is ordered from least to greatest. The mode is the value that appears most frequently, and the range is the difference between the maximum and minimum values.

Success on these questions requires a careful reading of tables and charts. You might be asked to determine how adding a new data point changes the mean or which group has a higher median based on a frequency table. According to the National Council of Teachers of Mathematics, understanding these foundational concepts is critical for developing higher-level data literacy. For students looking to build a strong foundation, visiting our ACT Prep hub provides a structured path through these mathematical requirements.

Solved Examples

1. A student takes four exams and earns scores of 85, 90, 75, and 90. What is the mean score of these exams?

1. Identify the sum of the scores: $85 + 90 + 75 + 90 = 340$.
2. Count the total number of exams: 4.
3. Divide the sum by the count: $\frac{340}{4} = 85$.
4. The mean score is 85.

2. Find the median of the following set of temperatures: $\{72^\circ, 68^\circ, 80^\circ, 75^\circ, 65^\circ, 70^\circ, 82^\circ\}$.

1. Arrange the numbers in ascending order: 65, 68, 70, 72, 75, 80, 82.
2. Identify the total count of values: 7 (an odd number).
3. Locate the middle value: The 4th value in the list is 72.
4. The median temperature is $72^\circ$.

3. A set of five numbers has a mean of 20. If four of the numbers are 15, 18, 22, and 25, what is the fifth number?

1. Use the mean formula: $\text{Mean} = \frac{ \text{Sum}}{ \text{Count}}$.
2. Calculate the required sum: $20 \times 5 = 100$.
3. Sum the known numbers: $15 + 18 + 22 + 25 = 80$.
4. Subtract the known sum from the total sum: $100 - 80 = 20$.
5. The fifth number is 20.

Practice Questions

1. A small business tracks the number of daily sales over a 5-day work week: 12, 15, 12, 18, and 13. What is the mode of this data set?

2. The heights of five basketball players in inches are 72, 75, 78, 72, and 83. What is the range of their heights?

3. A teacher calculates the average score of 10 students to be 82. If one student who scored 100 is removed from the data set, what happens to the mean?

4. In a survey of 6 people regarding the number of pets they own, the results were: 0, 1, 1, 2, 2, 6. What is the median number of pets owned?

5. If the mean of the set $\{x, 10, 15, 20\}$ is 15, what is the value of $x$?

6. A golfer records her scores for four rounds: 74, 72, 78, and 76. What is the mean score of her rounds?

7. A data set consists of the numbers: 5, 5, 10, 15, 20. If the number 40 is added to the set, which statistical measure (mean, median, or mode) will increase the most?

8. What is the range of the following set of numbers: $\{-10, -5, 0, 5, 10\}$?

9. A set of numbers is $\{4, 8, 12, 16, 20\}$. If every number in the set is increased by 5, what is the new mean?

10. Find the median of the set: $\{2, 14, 8, 10, 6, 12\}$.

Answers & Explanations

1. 12: The mode is the most frequent number. In the set {12, 15, 12, 18, 13}, the number 12 appears twice, while all others appear once.
2. 11: Range is calculated as Max − Min. Here, $83 - 72 = 11$.
3. The mean decreases: Since the removed score (100) is higher than the current average (82), the total sum drops significantly relative to the count, pulling the average down. For more practice with data trends, see our ACT Data Interpretation Practice Questions with Answers.
4. 1.5: To find the median of 0, 1, 1, 2, 2, 6, take the average of the two middle numbers: $\frac{1+2}{2} = 1.5$.
5. 15: The sum must be $15 \times 4 = 60$. Solving $x + 10 + 15 + 20 = 60$ gives $x + 45 = 60$, so $x = 15$.
6. 75: Sum the scores: $74 + 72 + 78 + 76 = 300$. Divide by 4: $\frac{300}{4} = 75$.
7. Mean: The original mean is 11, median is 10, and mode is 5. Adding 40 makes the new mean 15.8, the median 12.5, and the mode stays 5. The mean increases by 4.8, which is the largest jump. Analyzing these shifts is a common feature in ACT Statistics Interpretation Practice Questions with Answers.
8. 20: Range is $10 - (-10) = 10 + 10 = 20$.
9. 17: The original mean is 12. If you add 5 to every number, the mean also increases by 5. $12 + 5 = 17$.
10. 9: Ordered set: 2, 6, 8, 10, 12, 14. The middle two are 8 and 10. $\frac{8+10}{2} = 9$. You can find similar logic puzzles in our ACT Graph Analysis Practice Questions with Answers.

1. A set of data consists of the values 4, 4, 5, 10, and 12. Which of the following is the median?

• A4
• B5
• C7
• D12

Frequently Asked Questions

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

The mean is the calculated average of all numbers, while the median is the physical middle point of a sorted list. The ACT often tests your ability to choose which one is more affected by outliers, as the mean shifts more significantly than the median when extreme values are added.

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, you must take the average of the two middle numbers. For example, in the set {2, 4, 6, 8}, the middle numbers are 4 and 6, so the median is 5.

Can a data set have more than one mode?

Yes, a data set can be bimodal or multimodal if two or more values appear with the same highest frequency. If no value repeats, the set is said to have no mode.

Does the ACT allow calculators for statistics questions?

Calculators are permitted on the ACT Math section and can be very helpful for quickly summing large lists of numbers to find the mean. However, you must still know the definitions of median and mode, as calculators do not always have built-in functions for these in standard modes.

What is a weighted average in ACT statistics?

A weighted average occurs when some data points contribute more to the final average than others, often seen in GPA calculations or course grades. To solve these, multiply each value by its weight, sum those products, and divide by the total sum of the weights.