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SAT Math: Statistics and Probability (Drill 3)

Drill 3 · Math · Statistics and Probability

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About This Drill

SAT Math: Statistics and Probability (Drill 3) is a Math practice drill covering Statistics and Probability. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT statistics and probability questions cover measures of center and spread, interpreting standard deviation conceptually, computing probability using rules for independent and mutually exclusive events, and reading information from frequency tables and dot plots.

Questions & Explanations

Question 1. A data set has values {4, 8, 8, 10, 15}. If the value 15 is removed, which measure of center changes the most?

  • A) Mean ✓
  • B) Median
  • C) Mode
  • D) Range

Explanation: Original mean = 45/5 = 9. New mean = 30/4 = 7.5 (change of 1.5). Original median = 8, new median = 8 (no change). Mode stays 8. Mean changes the most.

Question 2. A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is NOT green?

  • A) 1/5
  • B) 2/5
  • C) 4/5 ✓
  • D) 3/10

Explanation: Total marbles = 10. Green = 2. P(not green) = 8/10 = 4/5.

Question 3. Data set A: {10, 10, 10, 10, 10}. Data set B: {2, 6, 10, 14, 18}. Both have the same mean. Which has the greater standard deviation?

  • A) Data set A
  • B) Data set B ✓
  • C) They are equal
  • D) Cannot be determined

Explanation: Set A has zero spread (all values identical), so SD = 0. Set B has values spread from 2 to 18 around the mean of 10, so its SD is greater.

Question 4. In a survey, 60% of respondents prefer coffee. If two respondents are chosen at random from a large population, what is the approximate probability both prefer coffee?

  • A) 0.36 ✓
  • B) 0.60
  • C) 1.20
  • D) 0.30

Explanation: For independent selections from a large population: P(both coffee) = 0.6 × 0.6 = 0.36.

Question 5. A student's test scores are 78, 85, 92, 88, and one unknown score. If the student needs a mean of 86 across all five tests, what score is needed on the fifth test?

  • A) 82
  • B) 86
  • C) 87 ✓
  • D) 88

Explanation: Need total = 86 × 5 = 430. Current sum = 78 + 85 + 92 + 88 = 343. Fifth score = 430 − 343 = 87.