Data Analysis Practice
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Data analysis questions test your ability to interpret information presented in tables, graphs, and charts. On the SAT, this domain (Problem-Solving and Data Analysis) makes up about 15% of math questions. On the ACT, similar questions appear throughout the math section and in the optional science section. These skills are essential for understanding real-world data.
What Is Data Analysis?
Data analysis involves examining, cleaning, and interpreting data to draw conclusions. On standardized tests, this includes reading graphs and tables, calculating statistics (mean, median, mode), working with ratios and percentages, and understanding probability.
Key Data Analysis Skills
1. Reading Tables
Tables organize data in rows and columns. To read a table:
- Identify what each row and column represents
- Check the units (percentages, dollars, quantities)
- Look for patterns, trends, or outliers
- Make sure you're reading the correct cell for the question
2. Reading Graphs
Common Graph Types
- Bar Graph: Compares quantities across categories
- Line Graph: Shows change over time (trends)
- Pie Chart: Shows parts of a whole (percentages)
- Scatter Plot: Shows relationship between two variables
- Histogram: Shows distribution/frequency of data
When reading any graph:
- Read the title to understand what data is shown
- Check axis labels and scales
- Note the units on each axis
- Look at the legend if multiple data sets are shown
3. Measures of Central Tendency
- Mean (Average): Sum of all values divided by the number of values
- Median: Middle value when data is ordered (or average of two middle values)
- Mode: Most frequently occurring value
- Range: Difference between highest and lowest values
When to Use Each Measure
Mean is affected by outliers. Median is better for skewed data or when outliers are present. Mode is useful for categorical data.
4. Percentages
Key percentage calculations:
- Finding a percentage: Part / Whole x 100
- Finding the part: Percentage x Whole / 100
- Percent change: (New - Original) / Original x 100
- Percent increase: If something increases by 20%, multiply by 1.20
- Percent decrease: If something decreases by 20%, multiply by 0.80
5. Ratios and Proportions
- Ratio: Comparison of two quantities (3:4 or 3/4)
- Proportion: Two equal ratios (a/b = c/d)
- Cross-multiplication: If a/b = c/d, then ad = bc
- Unit rate: Ratio with denominator of 1 (miles per hour, cost per item)
6. Probability
- Basic probability: P(event) = Favorable outcomes / Total outcomes
- Probability of NOT an event: P(not A) = 1 - P(A)
- Independent events: P(A and B) = P(A) x P(B)
- Probability is always between 0 and 1 (or 0% to 100%)
7. Scatter Plots and Correlation
- Positive correlation: As x increases, y increases (upward trend)
- Negative correlation: As x increases, y decreases (downward trend)
- No correlation: No clear pattern
- Line of best fit: Line that best represents the trend in the data
Test-Taking Strategy
Always read the question carefully BEFORE looking at the data. Know exactly what you're looking for. Then examine the data systematically. Watch out for traps like reading the wrong row/column or confusing labels.
Examples
Work through these SAT/ACT-style data analysis problems.
Example 1: Reading a Table
The table below shows the number of students enrolled in different subjects at a high school.
| Subject | Freshmen | Sophomores | Juniors | Seniors |
|---|---|---|---|---|
| Biology | 120 | 85 | 45 | 30 |
| Chemistry | 40 | 95 | 110 | 55 |
| Physics | 15 | 30 | 75 | 90 |
Question: What percentage of all physics students are seniors?
Solution:
Step 1: Find total physics students: 15 + 30 + 75 + 90 = 210
Step 2: Find percentage who are seniors: 90/210 x 100 = 42.9%
Answer: Approximately 43%
Example 2: Calculating Mean and Median
A student's quiz scores are: 72, 85, 88, 91, 94
Question: What is the mean score? What is the median score?
Solution:
Mean: (72 + 85 + 88 + 91 + 94) / 5 = 430 / 5 = 86
Median: Scores are already in order. The middle value (3rd of 5) is 88.
Answer: Mean = 86, Median = 88
Note: The median is higher than the mean because the outlier (72) pulls the mean down.
Example 3: Percent Change
A store's revenue increased from $45,000 in January to $54,000 in February.
Question: What was the percent increase in revenue?
Solution:
Percent change = (New - Original) / Original x 100
Percent change = (54,000 - 45,000) / 45,000 x 100
Percent change = 9,000 / 45,000 x 100
Percent change = 0.2 x 100 = 20%
Answer: 20% increase
Example 4: Probability
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
Question: If one marble is drawn at random, what is the probability it is NOT red?
Solution:
Total marbles: 5 + 3 + 2 = 10
Method 1: P(not red) = (blue + green) / total = (3 + 2) / 10 = 5/10 = 1/2
Method 2: P(not red) = 1 - P(red) = 1 - 5/10 = 1 - 1/2 = 1/2
Answer: 1/2 or 50%
Example 5: Ratio Problem
The ratio of boys to girls in a class is 3:5. If there are 40 students total, how many are boys?
Solution:
The ratio 3:5 means for every 3 boys, there are 5 girls.
Total parts = 3 + 5 = 8 parts
Each part = 40 / 8 = 5 students
Boys = 3 x 5 = 15
Answer: 15 boys
Check: Girls = 5 x 5 = 25. Total = 15 + 25 = 40. Ratio = 15:25 = 3:5.
Practice Problems
Apply your data analysis skills to these SAT/ACT-style questions.
1. The following data set shows test scores: 78, 82, 85, 85, 88, 92, 95. What is the mode?
Show Answer
B) 85 - The mode is the most frequently occurring value. 85 appears twice; all other values appear once.
2. A population of 2,500 increased by 8%. What is the new population?
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C) 2,700 - New population = 2,500 x 1.08 = 2,700. (Or: 8% of 2,500 = 200; 2,500 + 200 = 2,700)
3. A survey found that 45 out of 150 respondents prefer Brand A. What percentage prefer Brand A?
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A) 30% - Percentage = (45/150) x 100 = 0.30 x 100 = 30%
4. The ratio of cats to dogs at an animal shelter is 2:3. If there are 18 dogs, how many cats are there?
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B) 12 - Set up proportion: 2/3 = x/18. Cross-multiply: 3x = 36, so x = 12 cats.
5. A jar contains 8 red, 6 blue, and 4 yellow candies. What is the probability of randomly selecting a blue candy?
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B) 1/3 - Total candies = 18. P(blue) = 6/18 = 1/3. Note: D is equivalent to B but not simplified.
6. The mean of five numbers is 24. If four of the numbers are 20, 22, 25, and 28, what is the fifth number?
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C) 25 - If mean = 24 and there are 5 numbers, sum = 24 x 5 = 120. Sum of known numbers = 20 + 22 + 25 + 28 = 95. Fifth number = 120 - 95 = 25.
7. A stock price dropped from $80 to $60. What was the percent decrease?
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B) 25% - Percent change = (60 - 80)/80 x 100 = -20/80 x 100 = -25%. The decrease is 25%.
8. In a scatter plot showing hours studied vs. test scores, points generally go from lower-left to upper-right. This indicates:
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C) Positive correlation - When both variables increase together (lower-left to upper-right), there is a positive correlation. Note: Correlation does not prove causation.
9. A student scores 70, 75, 80, 85, and one more test. What must the fifth score be for the mean to equal 80?
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C) 90 - Target sum = 80 x 5 = 400. Current sum = 70 + 75 + 80 + 85 = 310. Fifth score = 400 - 310 = 90.
10. A coin is flipped 3 times. What is the probability of getting heads all 3 times?
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D) 1/8 - For independent events, multiply probabilities: (1/2) x (1/2) x (1/2) = 1/8.
Check Your Understanding
Review these key concepts before moving on.
1. When would the median be a better measure of central tendency than the mean?
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B) When the data has extreme outliers - Outliers significantly affect the mean but not the median. For skewed data or data with outliers, the median better represents the typical value.
2. To find what percent A is of B, you should:
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B) Divide A by B and multiply by 100 - Percentage = (Part/Whole) x 100. If A is the part and B is the whole, then A/B x 100 gives the percentage.
3. If two events are independent, the probability of both occurring is found by:
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B) Multiplying their probabilities - For independent events A and B, P(A and B) = P(A) x P(B).
4. A line of best fit on a scatter plot that slopes downward from left to right indicates:
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B) Negative correlation - When the line goes downward, as one variable increases, the other decreases - this is negative correlation.
Key Data Analysis Formulas
- Mean = Sum of values / Number of values
- Percent = (Part / Whole) x 100
- Percent change = (New - Original) / Original x 100
- Probability = Favorable outcomes / Total outcomes
- P(not A) = 1 - P(A)
- For independent events: P(A and B) = P(A) x P(B)
Next Steps
- Practice reading different types of graphs (bar, line, scatter, pie)
- Work on problems involving multiple steps (e.g., find mean, then use it to solve)
- Review ratio and proportion word problems
- Continue to the Question Bank for more practice problems