Bluebook SAT Test Problem Solving and Data Analysis 2 — Questions and Answers
Question 1: A box plot for a data set shows minimum=10, Q1=20, median=30, Q3=45, maximum=60. What is the interquartile range (IQR)?
- 25 (Correct answer)
- 50
- 15
- 30
Correct answer: 25
IQR = Q3 - Q1 = 45 - 20 = 25.
The IQR (Interquartile Range) measures the spread of the middle 50% of data. IQR = Q3 - Q1 = 45 - 20 = 25. The IQR is a robust measure of spread, unaffected by outliers. An outlier is typically defined as any value more than 1.5×IQR below Q1 or above Q3: below 20-37.5=-17.5 or above 45+37.5=82.5. The minimum (10) and maximum (60) are both within these bounds.
Question 2: A graph shows a strong positive correlation between hours of TV watched and snack consumption. What conclusion is best supported?
- As TV hours increase, snack consumption tends to increase (Correct answer)
- Watching TV causes increased snack consumption
- Snack consumption causes people to watch more TV
- There is no relationship between TV hours and snacks
Correct answer: As TV hours increase, snack consumption tends to increase
Correlation shows a relationship, not causation. The correct interpretation states the association without claiming cause.
A correlation describes the direction and strength of a relationship between two variables. A positive correlation means as one variable increases, the other tends to increase. However, correlation does not establish causation — we cannot conclude that TV watching causes snacking or vice versa from correlation alone. The correct statement describes only the observed association: as TV hours increase, snack consumption tends to increase. Options B and C incorrectly imply causation.
Question 3: A sample of 5 quiz scores is: 72, 85, 90, 78, 85. What is the mode?
- 85 (Correct answer)
- 72
- 82
- 78
Correct answer: 85
The mode is the most frequently occurring value. 85 appears twice; all others appear once.
The mode is the value that occurs most frequently. Looking at the scores: 72 (once), 78 (once), 85 (twice), 90 (once). Since 85 appears more often than any other value, the mode is 85. If no value repeated, there would be no mode. If two values tied, the data would be bimodal. The mode is the only measure of center that can be used for categorical data.
Question 4: A pie chart shows: Science 30%, Math 25%, English 20%, History 15%, Arts 10%. In a school of 400 students, how many study Math?
- 100 (Correct answer)
- 80
- 120
- 60
Correct answer: 100
Math students = 25% × 400 = 0.25 × 400 = 100.
From the pie chart, 25% of students study Math. With 400 total students: Math students = 25% × 400 = 0.25 × 400 = 100. Verify the percentages sum to 100%: 30+25+20+15+10 = 100% ✓. Pie charts are useful for showing proportions of a whole; each sector's area represents its percentage of the total.
Question 5: A study shows that children who read more books have higher test scores. Which statement is most accurate?
- Book reading is correlated with higher test scores (Correct answer)
- Book reading causes higher test scores
- Higher test scores cause children to read more
- Test scores and reading are unrelated
Correct answer: Book reading is correlated with higher test scores
Without a controlled experiment, we can only conclude correlation exists, not causation.
This is an observational study, not a controlled experiment. In observational studies, we can identify correlations but cannot establish causation because confounding variables may be present (e.g., both reading and test scores could be caused by family income or parental education). The most accurate and supported statement is that book reading is correlated with higher test scores — they tend to increase together. Statements claiming causation go beyond what the data supports.
Question 6: A histogram shows test scores: 60-70 (5 students), 70-80 (15 students), 80-90 (12 students), 90-100 (8 students). What percent of students scored 80 or above?
- 50% (Correct answer)
- 40%
- 60%
- 75%
Correct answer: 50%
Scored 80+: 12+8 = 20 students. Total = 5+15+12+8 = 40. Percentage = 20/40 = 50%.
Students scoring 80 or above: 12 (80-90) + 8 (90-100) = 20. Total students: 5+15+12+8 = 40. Percentage: 20/40 = 0.5 = 50%. This is a frequency histogram problem requiring adding appropriate class frequencies. Always calculate the total first to avoid calculation errors.
Question 7: The probability that event A occurs is 0.4 and the probability that event B occurs is 0.3. If A and B are independent events, what is P(A and B)?
- 0.12 (Correct answer)
- 0.70
- 0.10
- 0.58
Correct answer: 0.12
For independent events: P(A and B) = P(A) × P(B) = 0.4 × 0.3 = 0.12.
Two events are independent if the occurrence of one doesn't affect the probability of the other. For independent events: P(A∩B) = P(A)×P(B) = 0.4×0.3 = 0.12. Compare with P(A or B) = P(A)+P(B)-P(A∩B) = 0.4+0.3-0.12 = 0.58. Independence is a key assumption — if A and B were not independent, we would need conditional probability P(A|B) to find P(A∩B) = P(B)×P(A|B).
Question 8: A line of best fit for data has equation y = -2x + 50. For what value of x does the model predict y = 10?
- 20 (Correct answer)
- 30
- 15
- 10
Correct answer: 20
-2x + 50 = 10 → -2x = -40 → x = 20.
Setting y = 10 in the equation y = -2x+50: 10 = -2x+50. Subtracting 50: -40 = -2x. Dividing by -2: x = 20. The negative slope (-2) means as x increases, y decreases. This equation represents a declining trend — for every unit increase in x, y decreases by 2.
Bluebook SAT Test Problem Solving and Data Analysis 2
A box plot for a data set shows minimum=10, Q1=20, median=30, Q3=45, maximum=60.
What is the interquartile range (IQR)?