Medium ACT Data Analysis Practice Questions

Data analysis requires students to interpret, summarize, and draw conclusions from various datasets presented in tables, graphs, and charts. These skills are essential for success on the ACT Math and Science sections, where questions often ask you to identify trends or calculate values based on visual information. Understanding how to navigate these problems efficiently can significantly impact your composite score, especially when moving from basic identification to more complex interpretation. This guide provides specialized ACT Data Analysis practice questions designed to help you bridge the gap between simple reading and high-level reasoning.

Concept Explanation

ACT data analysis is the process of extracting meaningful information from quantitative displays and applying mathematical operations to that data. At its core, this involves three main stages: representation, interpretation, and extrapolation. Representation refers to how data is organized, such as in a scatterplot, bar graph, or frequency table. You must be able to identify the independent variable (usually on the x-axis) and the dependent variable (usually on the y-axis). Interpretation involves calculating statistical measures like mean, median, mode, and range, or determining the probability of an event based on a given sample. For a comprehensive look at these topics, many students start with ACT Prep to build a foundation in algebra and statistics. Extrapolation requires you to predict future values or identify relationships, such as direct or inverse proportions, by observing the slope or shape of a data set. Success in this area relies on your ability to ignore "distractor" data and focus only on the specific rows or columns mentioned in the question.

Solved Examples

1. Example 1: Calculating Weighted Averages
   A student’s final grade is calculated using three categories: Homework (20%), Quizzes (30%), and Exams (50%). If the student scored 90 on homework, 80 on quizzes, and 84 on exams, what is their final weighted average?
   1. Convert the percentages to decimals: 0.20, 0.30, and 0.50.
   2. Multiply each score by its corresponding weight: $90 \times 0.20 = 18$; $80 \times 0.30 = 24$; $84 \times 0.50 = 42$.
   3. Sum the results: $18 + 24 + 42 = 84$.
   4. The final weighted average is 84.
2. Example 2: Interpreting Scatterplots
   A scatterplot shows a negative correlation between the number of hours spent playing video games and test scores. If the line of best fit is represented by the equation $y = -5x + 95$, what is the predicted score for a student who plays for 4 hours?
   1. Identify the variables: $x$ is hours played (4) and $y$ is the predicted score.
   2. Substitute the value into the equation: $y = -5(4) + 95$.
   3. Perform the multiplication: $-20 + 95$.
   4. Calculate the final result: $75$.
3. Example 3: Probability from a Frequency Table
   A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, replaced, and then a second marble is drawn, what is the probability that both marbles are blue?
   1. Calculate the total number of marbles: $5 + 3 + 2 = 10$.
   2. Find the probability of drawing one blue marble: $\frac{3}{10}$.
   3. Since the marble is replaced, the probability for the second draw remains $\frac{3}{10}$.
   4. Multiply the probabilities for independent events: $\frac{3}{10} \times \frac{3}{10} = \frac{9}{100}$, or 0.09.

Practice Questions

1. A survey of 200 students asked about their favorite subjects. If 35% chose Math and 25% chose Science, how many more students chose Math than Science?

2. The set $S$ consists of the integers {4, 8, 12, 16, $x$}. If the mean of the set is 11, what is the value of $x$?

3. A biologist tracks the growth of a bacteria colony. On Day 1, there are 100 bacteria. The population doubles every 24 hours. Using the function $P(t) = 100(2)^t$, where $t$ is the number of days, how many bacteria will there be on Day 4?

4. A data set contains 10 values with a median of 15. If the largest value is increased by 20, what happens to the median of the data set?

5. In a group of 50 people, 30 like coffee, 25 like tea, and 10 like both. What is the probability that a person selected at random likes neither coffee nor tea?

6. Refer to the table below showing rainfall in inches for four months. What is the standard deviation range if the mean is 4.5 and the variance is 1.44?

Month	Rainfall (in)
April	3.2
May	5.1
June	4.8
July	4.9

7. A linear regression model for a company's profit $P$ in thousands of dollars based on the number of employees $n$ is given by $P = 12n - 50$. What does the value 12 represent in this context?

8. A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability that the spinner lands on a prime number OR a number greater than 6?

9. A table shows that for every 5 units of product A produced, 2 units of product B are produced. If the factory produces a total of 210 units in one day, how many units of product B were made?

10. If the range of a set of 5 consecutive even integers is $R$, and the mean is $M$, what is the value of $R$?

Answers & Explanations

1. Answer: 20
   First, calculate the number of students for each: Math is $0.35 \times 200 = 70$. Science is $0.25 \times 200 = 50$. The difference is $70 - 50 = 20$.
2. Answer: 15
   The mean formula is $\frac{ \text{sum}}{ \text{count}} = 11$. So, $\frac{4 + 8 + 12 + 16 + x}{5} = 11$. Multiplying both sides by 5 gives $40 + x = 55$. Subtracting 40 gives $x = 15$.
3. Answer: 800
   The question asks for Day 4, which means 3 days have passed since Day 1 (or $t=3$). Using the formula: $P(3) = 100(2)^3 = 100(8) = 800$.
4. Answer: It stays the same
   The median is the middle value of a sorted list. Changing the extreme values (the largest or smallest) does not affect the middle position of the data set.
5. Answer: 1/10 (or 0.1)
   Using the principle of inclusion-exclusion: $\text{Total liking either} = 30 + 25 - 10 = 45$. Since there are 50 people, $50 - 45 = 5$ people like neither. The probability is $\frac{5}{50} = \frac{1}{10}$.
6. Answer: 3.3 to 5.7
   Standard deviation is the square root of variance: $\sqrt{1.44} = 1.2$. One standard deviation from the mean is $4.5 \pm 1.2$, which results in the range 3.3 to 5.7.
7. Answer: The increase in profit (in thousands) for each additional employee
   In the linear equation $y = mx + b$, the slope $m$ represents the rate of change. Here, 12 is the slope, meaning profit increases by $12,000 for every 1 employee added.
8. Answer: 5/8
   Prime numbers are {2, 3, 5, 7}. Numbers greater than 6 are {7, 8}. The union of these sets is {2, 3, 5, 7, 8}. There are 5 favorable outcomes out of 8 total.
9. Answer: 60
   The ratio of A to B is 5:2. The total parts in the ratio are $5 + 2 = 7$. Divide the total production by the total parts: $210 / 7 = 30$. Product B is 2 parts: $2 \times 30 = 60$. For more practice with proportional reasoning, check out ACT Table Practice Questions.
10. Answer: 8
    Let the integers be $n, n+2, n+4, n+6, n+8$. The range is the largest minus the smallest: $(n+8) - n = 8$. The mean does not affect the range in this case.

1. If a data set has a mean of 20 and every value in the set is increased by 5, what is the new mean?

• A20
• B25
• C30
• D100

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. The median is the physical middle value of a data set when the numbers are arranged in ascending order.

How do I identify a line of best fit?

A line of best fit is a straight line that best represents the data on a scatterplot by minimizing the distance between the line and all data points. It typically passes through the center of the cluster of points, showing the overall trend.

What is weighted average and when is it used?

A weighted average is used when different data points contribute more to the final result than others, such as in GPA calculations or graded categories. You calculate it by multiplying each value by its weight (percentage) and summing the totals.

How does the ACT test probability?

The ACT tests probability by asking for the likelihood of an event occurring, usually expressed as a fraction or decimal. It often covers simple probability, independent events (multiplication), and mutually exclusive events (addition).

What are the most common graph types on the ACT?

Common graph types include bar graphs for categorical data, line graphs for trends over time, and scatterplots for showing relationships between two variables. You may also see ACT Graph Practice Questions involving pie charts or histograms.

Why is standard deviation important for data analysis?

Standard deviation measures the spread or dispersion of a data set relative to its mean. A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data is spread over a wider range.