ACT Data Analysis Practice Questions with Answers

Data analysis on the ACT requires students to interpret, summarize, and draw conclusions from various types of information presented in tables, graphs, and charts. These skills are essential for success in both the Math and Science sections of the exam. Students must be proficient in calculating measures of central tendency, such as mean, median, and mode, while also understanding how to extrapolate trends from visual data. Because the ACT emphasizes practical application, you will often need to combine multiple data points to solve a single problem.

Concept Explanation

ACT Data Analysis is the process of extracting meaningful information from quantitative and qualitative data sets to solve mathematical and scientific problems. This concept encompasses three primary areas: descriptive statistics, data interpretation, and probability. Descriptive statistics involve calculating the average (mean), the middle value (median), the most frequent value (mode), and the spread (range) of a data set. Data interpretation focuses on reading scatter plots, line graphs, bar charts, and frequency tables to identify relationships between variables. Finally, probability requires determining the likelihood of specific outcomes based on a given set of data. Success in this area depends on your ability to quickly identify the relevant numbers in a table and ignore "distractor" information that isn't necessary for the calculation. For a comprehensive overview of all exam sections, check out our ACT Prep hub.

Solved Examples

1. Example 1: Calculating the Mean
   A student took 5 tests and received scores of 82, 88, 91, 85, and 94. What is the mean score of these tests?
   1. Sum the scores: $82 + 88 + 91 + 85 + 94 = 440$.
   2. Divide the sum by the number of tests: $\frac{440}{5} = 88$.
   3. The mean score is 88.
2. Example 2: Finding the Median from a Table
   A survey asked 11 people how many books they read last month. The results are: 0, 0, 1, 2, 2, 3, 3, 4, 5, 7, 10. What is the median?
   1. Ensure the data is in ascending order (it is already ordered).
   2. Identify the middle term. Since there are 11 terms, the middle term is the $\frac{11+1}{2} = 6^{th}$ term.
   3. The 6th term in the list is 3.
   4. The median is 3.
3. Example 3: Interpreting a Scatter Plot
   A scatter plot shows a strong positive correlation between hours studied ($x$) and exam score ($y$). The line of best fit is given by the equation $y = 5x + 40$. Based on this model, what is the predicted score for a student who studies for 8 hours?
   1. Identify the independent variable value: $x = 8$.
   2. Substitute the value into the equation: $y = 5(8) + 40$.
   3. Calculate the result: $y = 40 + 40 = 80$.
   4. The predicted score is 80.

Practice Questions

1. A set of numbers consists of {4, 8, 12, 12, 15, 21}. If the number 30 is added to the set, which of the following measures will increase the most: mean, median, or mode?

2. In a group of 200 students, 120 are enrolled in Math, 80 are enrolled in Science, and 40 are enrolled in both. If a student is chosen at random, what is the probability they are enrolled in Math but NOT Science?

3. A line graph shows the population of a town over five years: Year 1: 5,000; Year 2: 5,500; Year 3: 6,100; Year 4: 6,800; Year 5: 7,600. What is the average annual increase in population from Year 1 to Year 5?

4. The table below shows the frequency of scores on a 10-point quiz. What is the mode of the scores?

Score	Frequency
6	2
7	5
8	8
9	4
10	1

5. If the mean of five consecutive integers is 24, what is the largest of these integers?

6. A bag contains 5 red marbles, 7 blue marbles, and 8 green marbles. If two marbles are drawn without replacement, what is the probability that both are green?

7. A researcher finds that the relationship between the temperature in degrees Celsius ($C$) and the chirping rate of a cricket ($R$) is $R = 4C - 20$. At what temperature would the cricket be expected to chirp 60 times per minute?

8. A data set has a mean of 15 and a range of 10. If every number in the set is multiplied by 3, what are the new mean and range?

9. A pie chart representing a budget of $4,000 shows that "Rent" accounts for $144^\circ$ of the circle. How much money is allocated to Rent?

10. The table below displays the results of a study on plant growth with different fertilizers. Based on the data, which fertilizer produced the highest average growth?

Fertilizer	Plant 1 (cm)	Plant 2 (cm)	Plant 3 (cm)
A	12	14	13
B	10	18	11
C	15	15	16

Answers & Explanations

1. Answer: Mean. Original mean: $\frac{4+8+12+12+15+21}{6} = 12$. New mean: $\frac{72+30}{7} \approx 14.57$ (increase of 2.57). Original median: 12. New median: 12 (no change). Original mode: 12. New mode: 12 (no change). Use our AI Question Generator to practice more set-based statistics.
2. Answer: 0.4 (or 40%). Total students enrolled in Math is 120. 40 of these are also in Science. Therefore, $120 - 40 = 80$ students are in Math ONLY. Probability = $\frac{80}{200} = 0.4$.
3. Answer: 650. Total increase = $7,600 - 5,000 = 2,600$. The time span from Year 1 to Year 5 is 4 years. Average increase = $\frac{2,600}{4} = 650$ people per year.
4. Answer: 8. The mode is the value with the highest frequency. Score 8 occurs 8 times, which is more than any other score.
5. Answer: 26. Let the integers be $x-2, x-1, x, x+1, x+2$. The mean is the middle term $x$, so $x = 24$. The largest integer is $x+2 = 26$.
6. Answer: $\frac{14}{95}$. Total marbles = 20. Probability of first green = $\frac{8}{20}$. Probability of second green = $\frac{7}{19}$. $\frac{8}{20} \times \frac{7}{19} = \frac{2}{5} \times \frac{7}{19} = \frac{14}{95}$.
7. Answer: 20. Set $R = 60$ and solve for $C$: $60 = 4C - 20 \rightarrow 80 = 4C \rightarrow C = 20$.
8. Answer: Mean = 45, Range = 30. When every value in a set is multiplied by a constant $k$, the mean, median, and range are all multiplied by $k$. $15 \times 3 = 45$ and $10 \times 3 = 30$.
9. Answer: $1,600. A circle has $360^\circ$. The fraction for rent is $\frac{144}{360} = 0.4$. Total budget $\$4,000 \times 0.4 = \$1,600$.
10. Answer: Fertilizer C. Average A: $\frac{12+14+13}{3} = 13$. Average B: $\frac{10+18+11}{3} = 13$. Average C: $\frac{15+15+16}{3} = 15.33$. Fertilizer C is the highest.

1. A set of data contains the values {5, 5, 10, 15, 20}. If the value 20 is changed to 25, which of the following must change?

• AThe mode
• BThe median
• CThe mean
• DThe total count of numbers

Frequently Asked Questions

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

The mean is the arithmetic average calculated by dividing the sum of all values by the total count, while the median is the middle value when the data is ordered from least to greatest. The ACT often tests your ability to determine which measure is more affected by "outliers," or extreme values.

How do I read a scatter plot for the Science section?

Look at the axes to identify the independent and dependent variables, then observe the general direction of the data points. If the points trend upward from left to right, it is a positive correlation; if they trend downward, it is a negative correlation.

What is a weighted average and how is it calculated?

A weighted average accounts for the relative importance or frequency of different values in a data set. To calculate it, multiply each value by its weight (or frequency), sum those products, and divide by the total sum of the weights.

Are probability questions common in ACT Data Analysis?

Yes, basic probability—the number of successful outcomes divided by the total number of possible outcomes—appears frequently. You may also encounter compound probability, which requires multiplying the probabilities of two or more independent events.

How can I improve my speed on data interpretation questions?

Practice identifying the specific labels and units on graphs before reading the question. Many students lose time by trying to understand every detail of a chart when the question only requires one specific data point. Using tools like the AI Exam Simulator can help you build this speed under timed conditions.

How does range differ from standard deviation?

Range is a simple measure of the total spread (maximum minus minimum), whereas standard deviation measures how much the values in a data set vary from the mean. While you rarely have to calculate standard deviation on the ACT, you should understand that a higher standard deviation means the data is more spread out.