Question bank
Data & Statistics Questions.
Ratios, rates, proportional reasoning, probability, statistical concepts, and data distributions.
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A recipe calls for 3 cups of flour to make 12 cookies. How many cups are needed to make 36 cookies?
- 6
- 8
- 9 ✓
- 12
Explanation
36/12 = 3, so multiply by 3: 3 × 3 = 9 cups.
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A car travels 240 miles in 4 hours. At the same rate, how far does it travel in 7 hours?
- 300
- 360
- 420 ✓
- 480
Explanation
Rate = 240/4 = 60 mph. Distance = 60 × 7 = 420 miles.
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A map uses a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?
- 75 miles
- 82.5 miles
- 87.5 miles ✓
- 90 miles
Explanation
3.5 × 25 = 87.5 miles.
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A store sells juice in 12 oz bottles for $2.40 or 20 oz bottles for $3.60. Which size is the better value, and by how much per ounce?
- 12 oz, by $0.02 per oz
- 20 oz, by $0.01 per oz
- 20 oz, by $0.02 per oz ✓
- Same value per ounce
Explanation
12 oz: $2.40/12 = $0.20/oz. 20 oz: $3.60/20 = $0.18/oz. The 20 oz bottle is better by $0.02/oz.
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A shirt costs $40 and is on sale for 25% off. What is the sale price?
- $25
- $28
- $30 ✓
- $32
Explanation
Discount = 25% of $40 = $10. Sale price = $40 − $10 = $30.
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A TV was originally $500 and is now $425. What is the percent decrease?
- 10%
- 12%
- 15% ✓
- 17%
Explanation
Percent decrease = (500 − 425)/500 × 100 = 75/500 × 100 = 15%.
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A student scored 78 out of 120 points. What percent did she score?
- 60%
- 62%
- 65% ✓
- 70%
Explanation
78/120 × 100 = 65%.
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After a 20% increase, a price is $84. What was the original price?
- $60
- $65
- $70 ✓
- $75
Explanation
Original × 1.20 = 84 → Original = 84/1.20 = $70.
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A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?
- 1/5
- 3/10 ✓
- 1/2
- 3/5
Explanation
P(blue) = 3/10.
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One card is drawn from a standard 52-card deck. What is the probability of drawing a face card (J, Q, or K)?
- 1/13
- 3/13 ✓
- 4/13
- 1/4
Explanation
There are 12 face cards in a deck of 52. P = 12/52 = 3/13.
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A class of 40 students includes 15 boys who like math, 5 boys who do not, 10 girls who like math, and 10 girls who do not. What is the probability that a randomly chosen student is a girl who likes math?
- 1/5
- 1/4 ✓
- 1/2
- 10/15
Explanation
10 girls who like math out of 40 students: P = 10/40 = 1/4.
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P(A) = 0.4 and P(B) = 0.3. If A and B are independent events, what is P(A and B)?
- 0.07
- 0.10
- 0.12 ✓
- 0.70
Explanation
For independent events: P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
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The data set is 4, 7, 7, 9, 13. What is the median?
- 7 ✓
- 8
- 9
- 10
Explanation
The data is already in order. The middle value (3rd of 5) is 7.
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The data set is 2, 5, 7, 8, 8, 10. What is the mean?
- 6.5
- 6.67 ✓
- 7
- 8
Explanation
Sum = 2 + 5 + 7 + 8 + 8 + 10 = 40. Mean = 40/6 ≈ 6.67.
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Which measure of center is most affected by an extreme outlier?
- Mean ✓
- Median
- Mode
- Range
Explanation
The mean uses all values in its calculation, so a very large or very small outlier pulls it significantly. The median is resistant to outliers.
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What does the standard deviation of a data set measure?
- The average value of the data
- The middle value of the data
- The most frequent value in the data
- The spread of data values around the mean ✓
Explanation
Standard deviation measures how much the data values vary from the mean — it quantifies spread.
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A bar chart shows January sales: 200, February: 150, March: 250. What is the total for these three months?
- 500
- 550
- 600 ✓
- 650
Explanation
200 + 150 + 250 = 600.
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A line of best fit for study hours (x) and test score (y) is y = 5x + 60. What score does the model predict for 8 hours of study?
- 80
- 90
- 95
- 100 ✓
Explanation
y = 5(8) + 60 = 40 + 60 = 100.
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A histogram shows 30% of 200 students scored 70–80, 45% scored 80–90, and 25% scored 90–100. How many students scored in the 80–90 range?
- 70
- 80
- 90 ✓
- 100
Explanation
45% of 200 = 0.45 × 200 = 90 students.
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A study finds a correlation coefficient of −0.85 between hours of sleep and reaction time. What does this indicate?
- No relationship
- Weak positive relationship
- Weak negative relationship
- Strong negative relationship ✓
Explanation
A value of −0.85 is close to −1, indicating a strong negative correlation: more sleep is associated with lower (faster) reaction times.
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A runner completes 5 laps in 20 minutes. How long does it take to complete 8 laps at the same pace?
- 28 min
- 30 min
- 32 min ✓
- 36 min
Explanation
Rate = 20/5 = 4 min per lap. Time for 8 laps = 8 × 4 = 32 minutes.
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A class has 12 boys and 18 girls. What is the ratio of boys to the total number of students?
- 2:3
- 2:5 ✓
- 3:5
- 3:2
Explanation
Total = 30. Ratio of boys to total = 12:30 = 2:5.
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A printer prints 240 pages in 6 minutes. How many pages does it print in 25 minutes?
- 800
- 900
- 1,000 ✓
- 1,200
Explanation
Rate = 240/6 = 40 pages/min. Pages in 25 min = 40 × 25 = 1,000.
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In a survey, 3 out of every 8 people prefer tea. In a group of 320 people, how many prefer tea?
- 100
- 110
- 120 ✓
- 130
Explanation
(3/8) × 320 = 120 people.
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Two workers can complete a job in 6 hours together. Worker A alone takes 10 hours. How long does Worker B alone take?
- 12 hours
- 15 hours ✓
- 18 hours
- 20 hours
Explanation
Combined rate = 1/6 jobs/hr. A's rate = 1/10. B's rate = 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15. B alone takes 15 hours.
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A jacket costs $80. It is discounted by 15%. What is the discount amount?
- $10
- $12 ✓
- $14
- $16
Explanation
Discount = 15% of $80 = 0.15 × 80 = $12.
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A population grew from 4,000 to 4,500. What was the percent increase?
- 10%
- 11.1%
- 12.5% ✓
- 15%
Explanation
Percent increase = (500/4000) × 100 = 12.5%.
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An item is marked up 40% from its wholesale price, then discounted 20% at a sale. What is the overall percent change from the wholesale price?
- 8% decrease
- 8% increase
- 12% increase ✓
- 20% increase
Explanation
Let wholesale = 100. After 40% markup: 140. After 20% discount: 140 × 0.80 = 112. Net change = +12%.
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A bank account earns 5% simple interest per year. After how many years will an initial deposit of $600 grow to $750?
- 3
- 4
- 5 ✓
- 6
Explanation
Simple interest: I = Prt. 150 = 600 × 0.05 × t → t = 150/30 = 5 years.
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A price is reduced by 30%, then reduced by another 20%. What is the total percentage decrease from the original price?
- 44% ✓
- 50%
- 54%
- 56%
Explanation
Let original = 100. After 30% off: 70. After 20% off that: 70 × 0.80 = 56. Total decrease = 100 − 56 = 44%.
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A fair die is rolled once. What is the probability of rolling a number greater than 4?
- 1/6
- 1/3 ✓
- 1/2
- 2/3
Explanation
Numbers greater than 4 on a standard die: 5 and 6 — two outcomes. P = 2/6 = 1/3.
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A bag has 4 red, 5 blue, and 1 green marble. One marble is drawn and not replaced; then a second is drawn. What is the probability both are red?
- 4/25
- 2/15 ✓
- 4/10
- 1/5
Explanation
P(1st red) = 4/10. P(2nd red | 1st red) = 3/9. P(both red) = (4/10)(3/9) = 12/90 = 2/15.
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In a class of 30 students, 18 play sports and 12 do not. If two students are chosen at random, what is the probability both play sports?
- 51/145 ✓
- 9/25
- 3/5
- 18/30
Explanation
P = (18/30) × (17/29) = 306/870 = 51/145.
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A spinner has 8 equal sections numbered 1–8. What is the probability of spinning an even number or a number greater than 5?
- 5/8 ✓
- 6/8
- 7/8
- 1/2
Explanation
Evens: {2, 4, 6, 8}. Greater than 5: {6, 7, 8}. Union: {2, 4, 6, 7, 8} — 5 outcomes. P = 5/8.
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Events A and B are mutually exclusive. P(A) = 0.35 and P(B) = 0.25. What is P(A or B)?
- 0.0875
- 0.10
- 0.60 ✓
- 0.875
Explanation
For mutually exclusive events: P(A or B) = P(A) + P(B) = 0.35 + 0.25 = 0.60.
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The data set is 3, 5, 7, 7, 9, 11. What is the mode?
- 5
- 6
- 7 ✓
- 9
Explanation
The mode is the most frequently occurring value. 7 appears twice; all others appear once.
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The data set is 10, 14, 18, 22, 26. What is the interquartile range (IQR)?
- 8
- 10
- 12 ✓
- 16
Explanation
Q1 = 12 (midpoint of lower half: 10, 14), Q3 = 24 (midpoint of upper half: 22, 26). IQR = 24 − 12 = 12.
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Which of the following best describes a data distribution that is skewed right?
- The mean is less than the median
- The mean equals the median
- The mean is greater than the median ✓
- The mode is greater than the mean
Explanation
In a right-skewed (positively skewed) distribution, the long tail is on the right and the mean is pulled above the median by the high outliers.
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A data set has a mean of 50 and a standard deviation of 5. A new data point of 65 is added. Compared to the original set, the new mean will be ___.
- Higher, because 65 > 50 ✓
- Lower, because adding data decreases the mean
- Unchanged, because one point does not affect the mean
- The same as the median
Explanation
Adding a value (65) above the current mean (50) will pull the mean upward, so the new mean will be higher.
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A data set has values 4, 6, 8, 10, 12. If every value is multiplied by 3, what happens to the mean and standard deviation?
- Mean triples; standard deviation stays the same
- Mean triples; standard deviation triples ✓
- Mean stays the same; standard deviation triples
- Both stay the same
Explanation
Multiplying every value by a constant k multiplies both the mean and the standard deviation by k. So both triple.
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A pie chart shows that 35% of students prefer math, 25% prefer science, and 40% prefer English. In a class of 80 students, how many prefer math?
- 20
- 24
- 28 ✓
- 32
Explanation
35% of 80 = 0.35 × 80 = 28.
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A scatter plot shows that as x increases, y tends to decrease. Which best describes the correlation?
- Positive correlation
- Negative correlation ✓
- No correlation
- Perfect positive correlation
Explanation
When one variable increases and the other decreases, the correlation is negative.
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A two-way table shows: 40 students passed Math, 30 passed English, and 15 passed both. Using the inclusion-exclusion principle, how many passed at least one subject?
- 55 ✓
- 60
- 65
- 70
Explanation
P(Math or English) = 40 + 30 − 15 = 55.
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A survey of 200 people found that 120 own a car, 80 own a bike, and 40 own both. What percentage own neither?
- 10%
- 15%
- 20% ✓
- 25%
Explanation
Own at least one = 120 + 80 − 40 = 160. Own neither = 200 − 160 = 40. Percent = 40/200 × 100 = 20%.
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A line of best fit for a data set is y = −3x + 90, where x is the number of absences and y is the final grade. What does the slope −3 indicate?
- For each additional absence, the predicted grade increases by 3 points
- For each additional absence, the predicted grade decreases by 3 points ✓
- The predicted grade when there are 0 absences is −3
- The predicted grade when there are 0 absences is 3
Explanation
The slope represents the rate of change. A slope of −3 means each additional absence is associated with a 3-point decrease in the predicted grade.
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The scores on a quiz are 8, 9, 7, 10, and 6. What is the mean score?
- 7
- 8 ✓
- 9
- 10
Explanation
Mean = (8 + 9 + 7 + 10 + 6) / 5 = 40 / 5 = 8.
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A bag contains 4 red marbles and 6 blue marbles. If one marble is drawn at random, what is the probability it is red?
- 1/4
- 2/5 ✓
- 1/2
- 3/5
Explanation
Probability = favorable outcomes / total outcomes = 4 / 10 = 2/5.
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What is the median of the data set {3, 7, 9, 1, 5}?
- 3
- 5 ✓
- 7
- 9
Explanation
Sort the data: 1, 3, 5, 7, 9. The middle value (3rd of 5) is 5.
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A data set has a mean of 50 and a standard deviation of 5. Which value is most likely an outlier?
- 45
- 52
- 58
- 68 ✓
Explanation
Values more than 2 standard deviations from the mean (outside 40–60) are potential outliers. 68 = 50 + 3.6 × 5, well beyond 2 standard deviations, making it the most likely outlier.
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In a data set {10, 12, 14, 16, 18, 20}, the value 20 is replaced by 50. Which measures of the data are affected?
- Mean only
- Median only
- Mean and range ✓
- Median and range
Explanation
The mean changes because the sum increases. The range changes from 10 to 40. The median (average of 14 and 16 = 15) is unaffected because 50 is still the largest value.
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A data set has values 4, 8, 6, 4, 10, 4, 7. What is the mode?
- 4 ✓
- 6
- 7
- 8
Explanation
The mode is the value that appears most often. 4 appears three times — more than any other value.
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A class of 30 students was surveyed about their favorite subject. 12 chose Math. What percentage chose Math?
- 30%
- 35%
- 40% ✓
- 45%
Explanation
Percentage = (12 / 30) × 100 = 40%.
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A spinner has 8 equal sections numbered 1 through 8. What is the probability of landing on a number greater than 5?
- 1/4
- 3/8 ✓
- 1/2
- 5/8
Explanation
Numbers greater than 5 are 6, 7, 8 — three out of eight sections. P = 3/8.
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The ages of five people are 22, 25, 19, 31, and 23. What is the range of their ages?
- 9
- 10
- 11
- 12 ✓
Explanation
Range = maximum − minimum = 31 − 19 = 12.
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In a bar chart, the bar for "Science" reaches a height of 45 and the bar for "Art" reaches 15. How many times taller is the Science bar than the Art bar?
- 2
- 3 ✓
- 4
- 5
Explanation
45 ÷ 15 = 3. The Science bar is 3 times taller.
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The box plot for a data set shows a minimum of 10, Q1 of 20, median of 30, Q3 of 45, and maximum of 60. What is the interquartile range (IQR)?
- 15
- 20
- 25 ✓
- 30
Explanation
IQR = Q3 − Q1 = 45 − 20 = 25.
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A school records the number of books read by students: {2, 3, 3, 4, 5, 6, 6, 6, 8, 9}. What is the median?
- 5
- 5.5 ✓
- 6
- 6.5
Explanation
With 10 values, the median is the average of the 5th and 6th values: (5 + 6) / 2 = 5.5.
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A fair coin is flipped twice. What is the probability of getting heads both times?
- 1/4 ✓
- 1/3
- 1/2
- 3/4
Explanation
Each flip is independent. P(HH) = P(H) × P(H) = 1/2 × 1/2 = 1/4.
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A sample of 5 test scores has a mean of 80. If a sixth score of 92 is added, what is the new mean?
- 82 ✓
- 83
- 84
- 85
Explanation
Original total = 5 × 80 = 400. New total = 400 + 92 = 492. New mean = 492 / 6 = 82.
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A histogram shows that 15 students scored in the 70–79 range, 25 scored in the 80–89 range, and 10 scored in the 90–99 range. What fraction of students scored 80 or above?
- 1/2
- 7/10 ✓
- 3/5
- 2/5
Explanation
Total students = 15 + 25 + 10 = 50. Students scoring 80+ = 25 + 10 = 35. Fraction = 35/50 = 7/10.
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A survey finds that 60% of people prefer coffee, 30% prefer tea, and 10% prefer neither. If 200 people were surveyed, how many prefer tea?
- 30
- 40
- 50
- 60 ✓
Explanation
30% of 200 = 0.30 × 200 = 60 people prefer tea.
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The line of best fit for a data set is y = 4x + 10. What does the y-intercept 10 represent?
- The rate of change of y per unit of x
- The predicted value of y when x = 0 ✓
- The predicted value of x when y = 0
- The correlation coefficient
Explanation
The y-intercept is the predicted value of y when x = 0, meaning the starting value when the input is zero.
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A data set of 8 values has a mean of 15. If one value of 7 is removed, what is the new mean?
- 15
- 16 ✓
- 17
- 18
Explanation
Original total = 8 × 15 = 120. Remove 7: new total = 113. New mean = 113 / 7 = 16.14... ≈ 16.
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A study found a strong positive correlation (r = 0.92) between hours of exercise per week and resting heart rate reduction. Which conclusion is most appropriate?
- Exercise causes heart rate reduction
- Heart rate reduction causes more exercise
- More exercise is associated with greater heart rate reduction ✓
- The variables have no meaningful relationship
Explanation
Correlation shows association, not causation. The correct interpretation is that more exercise is associated with greater heart rate reduction.
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A bag contains 5 red, 3 blue, and 2 green marbles. Two marbles are drawn without replacement. What is the probability that both are red?
- 1/5
- 2/9 ✓
- 1/4
- 5/18
Explanation
P(both red) = (5/10) × (4/9) = 20/90 = 2/9.
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A data set is normally distributed with mean 100 and standard deviation 15. Approximately what percentage of data falls between 85 and 115?
- 34%
- 50%
- 68% ✓
- 95%
Explanation
85 and 115 are each exactly one standard deviation from the mean (100 ± 15). By the empirical rule, approximately 68% of data falls within one standard deviation of the mean.
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The table below shows the results of a poll. Of 120 voters polled, 45 were under 40 and voted Yes, 30 were under 40 and voted No, 25 were 40+ and voted Yes, and 20 were 40+ and voted No. What is the probability that a randomly selected voter who voted Yes is under 40?
- 3/7
- 9/14 ✓
- 3/5
- 5/7
Explanation
Total Yes votes = 45 + 25 = 70. Of those, 45 were under 40. P(under 40 | Yes) = 45/70 = 9/14.
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A researcher increases the sample size of a study from 50 to 200. What is the most likely effect on the margin of error?
- The margin of error doubles
- The margin of error is halved ✓
- The margin of error stays the same
- The margin of error increases by a factor of 4
Explanation
Margin of error is proportional to 1/√n. Quadrupling the sample size (50→200) multiplies 1/√n by 1/√4 = 1/2, so the margin of error is halved.
-
A data set {5, 8, 12, 15, x} has a mean of 11. What is the value of x?
- 13
- 14
- 15 ✓
- 16
Explanation
Mean = (5 + 8 + 12 + 15 + x) / 5 = 11 → 5 + 8 + 12 + 15 + x = 55 → 40 + x = 55 → x = 15.
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A scatterplot shows data with the line of best fit y = 2.5x + 4. A point on the plot is at (6, 20). What is the residual for this point?
- −1
- 0
- 1 ✓
- 2
Explanation
Predicted value at x = 6: y = 2.5(6) + 4 = 15 + 4 = 19. Residual = observed − predicted = 20 − 19 = 1.
How to practice SAT Math Data & Statistics questions
Data & Statistics — officially "Problem-Solving and Data Analysis" — is about 15% of the section and tends to be the most approachable once you know what each question is really asking. The set below covers ratios and rates, percentages, probability, measures of center, and reading graphs and two-way tables. The trap here is rarely the math; it is misreading which quantity the question wants. Slow down on the wording and these become reliable points.
Study tips for Data & Statistics
- On two-way table questions, re-read to confirm whether you need a row rate, a column rate, or a share of the overall total before dividing.
- Convert every percent to a decimal and multiply for "percent of a percent" problems instead of adding percentages.
- Ask whether mean or median fits the question — the SAT specifically tests knowing that outliers pull the mean but not the median.
- For scatterplots and lines of best fit, many questions just want you to read a y-value at a given x. Do not overcomplicate it.
Common mistakes to avoid
- Dividing by the wrong total in a two-way table (row versus column versus grand total).
- Computing percent change from the new value instead of the original value.
- Reporting the mean when a question about a skewed data set is really testing the median.
Data & Statistics practice: frequently asked questions
Is Data & Statistics the easiest SAT Math domain?
For many students, yes — the arithmetic is usually straightforward. The difficulty lives in careful reading of graphs, tables, and question wording rather than in hard computation.
What statistics do I actually need to know?
Mean, median, mode, range, and a conceptual sense of standard deviation (spread). You will not compute standard deviation by hand, but you should know that a wider spread means a larger value.
How do I get faster at data questions?
Practice extracting the one number the question needs before doing any math. Most mistakes here are reading errors, which drills like these questions fix quickly.