DSAT Data Analysis 3 — Questions and Answers
Question 1: Of 80 students who play sports, 60 get good grades. Of 120 who don't play sports, 40 get good grades. What fraction of all 200 students get good grades?
- 1/2 (Correct answer)
- 2/5
- 3/10
- 3/5
Correct answer: 1/2
Total with good grades = 60 + 40 = 100 out of 200 students = 100/200 = 1/2.
Question 2: A city's population was 50,000 in 2000 and 80,000 in 2020. What was the percent increase over this period?
- 30%
- 37.5%
- 60% (Correct answer)
- 62.5%
Correct answer: 60%
Percent increase = (80,000 − 50,000)/50,000 × 100 = 30,000/50,000 × 100 = 60%.
Question 3: A random sample of 500 voters shows 55% support a ballot measure, but the true population support is 52%. What best explains the 3-point difference?
- The survey was intentionally biased
- The difference is due to sampling variability (Correct answer)
- The population proportion must be incorrect
- 55% is always more accurate than 52%
Correct answer: The difference is due to sampling variability
Random samples naturally vary from the true population value; this difference is expected sampling variability.
Question 4: Annual sales (in millions) over four years: $4M, $6M, $5M, $8M. What is the mean annual sales?
- $5M
- $5.75M (Correct answer)
- $6M
- $6.5M
Correct answer: $5.75M
Mean = (4 + 6 + 5 + 8) / 4 = 23 / 4 = $5.75M.
Question 5: A study reports a drug reduces cholesterol by an average of 15 points with a p-value of 0.03. Which conclusion is most appropriate?
- The drug has no effect on cholesterol
- The result is statistically significant at the 0.05 level (Correct answer)
- The drug reduces cholesterol by exactly 15 points in all patients
- The study must be repeated before any conclusion can be drawn
Correct answer: The result is statistically significant at the 0.05 level
A p-value of 0.03 is less than 0.05, so the result is statistically significant at the 5% significance level.
Question 6: A histogram is right-skewed. Which statement about its mean and median is most likely true?
- Mean < Median
- Mean = Median
- Mean > Median (Correct answer)
- Neither can be determined
Correct answer: Mean > Median
In a right-skewed distribution, the long right tail pulls the mean above the median.
Question 7: Ice cream sales and drowning rates both rise in summer. A reporter claims ice cream causes drowning. What is the flaw in this reasoning?
- The data is fabricated
- The reporter confused mean and median
- Hot weather is a confounding variable causing both to rise (Correct answer)
- Drowning rates never correlate with any sales data
Correct answer: Hot weather is a confounding variable causing both to rise
Hot weather drives both ice cream consumption and swimming activity, making temperature the confounding variable.
DSAT Data Analysis 3
Of 80 students who play sports, 60 get good grades.
Of 120 who don't play sports, 40 get good grades.
What fraction of all 200 students get good grades?