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SAT Math: Statistics and Probability (Drill 1)

Drill 1 · Math · Statistics and Probability

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About This Drill

SAT Math: Statistics and Probability (Drill 1) 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 calculating mean, median, and mode, interpreting range and standard deviation as measures of spread, computing theoretical and experimental probability, and reading data from histograms and two-way tables.

Questions & Explanations

Question 1. The data set {4, 7, 9, 10, 15} represents the number of books read by five students last month. What is the mean of this data set?

  • A) 7
  • B) 9 ✓
  • C) 10
  • D) 11

Explanation: Mean = (4 + 7 + 9 + 10 + 15) / 5 = 45/5 = 9.

Question 2. A teacher recorded the test scores of nine students: 72, 75, 78, 80, 82, 84, 85, 88, 90. If a tenth student scores 40, which measure of central tendency will be most affected?

  • A) Median
  • B) Mode
  • C) Mean ✓
  • D) None of the above

Explanation: The mean is calculated by summing all values and dividing by the count, so an outlier like 40 pulls the mean down. The median is resistant to outliers.

Question 3. A bag contains 8 red marbles, 5 blue marbles, and 7 green marbles. If one marble is selected at random, what is the probability that it is blue?

  • A) 1/4 ✓
  • B) 1/5
  • C) 5/15
  • D) 5/8

Explanation: Total marbles = 8 + 5 + 7 = 20. Probability of blue = 5/20 = 1/4.

Question 4. Data set A: {50, 50, 50, 50}. Data set B: {20, 40, 60, 80}. Both sets have a mean of 50. Which statement is true?

  • A) Set A has a greater standard deviation than Set B.
  • B) Both sets have the same standard deviation.
  • C) Neither set has a standard deviation that can be calculated.
  • D) Set B has a greater standard deviation than Set A. ✓

Explanation: Set A has all identical values (no spread), so its standard deviation is 0. Set B has values ranging from 20 to 80, so its standard deviation is much greater.

Question 5. A school principal wants to estimate the average number of hours all students spend studying per week. The principal surveys only students in honors classes. Which best describes the limitation?

  • A) The sample size is too small.
  • B) The sample is not representative of all students at the school. ✓
  • C) The survey question is biased.
  • D) The results cannot be expressed as an average.

Explanation: Honors students are likely not representative of the entire student body; they may study more than average. This is a sampling bias problem.