SAT Math Practice Test: Statistics and Probability
- Statistics and Probability
- 10 questions
- 15 minutes
These 10 questions practice the statistics and probability skills of the SAT Problem-Solving and Data Analysis domain. In probability questions, find the group you are choosing from first; it is the denominator.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
4, 7, 7, 9, 13
What is the mean of the data set shown?
Correct answer: B
The sum is 40 and there are 5 values, so the mean is 40 ÷ 5 = 8. The choice 7 is the median and the mode.
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Question 2
12, 15, 15, 18, 20
The value 60 is added to the data set shown. Which statement correctly describes the change in the mean and median?
Correct answer: C
The mean rises from 16 to 140 ÷ 6 ≈ 23.3, while the median rises only from 15 to (15 + 18) ÷ 2 = 16.5. The median does change, because the middle of an even-sized set is the average of two values.
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Question 3
The table shows the results of a survey that asked 200 people whether they prefer tea or coffee.
Tea Coffee Total Under 30 36 54 90 30 or older 66 44 110 Total 102 98 200 If a person who prefers tea is chosen at random, what is the probability that the person is under 30?
Correct answer: B
The choice is made only among the 102 tea drinkers, and 36 of them are under 30, so the probability is 36/102 = 6/17. The choice 9/50 is 36/200, which divides by all people surveyed.
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Question 4
Set A: 10, 10, 10, 10, 10
Set B: 2, 6, 10, 14, 18Which statement about the two data sets is true?
Correct answer: D
Both sets have a mean of 10. Set A has a standard deviation of 0 because every value equals the mean, while the values in Set B are spread out, so Set B has the greater standard deviation.
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Question 5
A polling group surveyed a random sample of 400 voters in a city about a new transit plan. Of those surveyed, 58% supported the plan. The margin of error for this estimate is 4 percentage points. Which conclusion is best supported by the survey?
Correct answer: A
The margin of error gives a plausible range for the whole city: 58% ± 4%, or 54% to 62%. The sample came only from the city, so it supports no conclusion about the state, and a sample estimate never gives an exact value.
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Question 6
A teacher modeled the relationship between the number of hours x a student studied and the student's test score y with the line of best fit y = 2.5x + 62. Which is the best interpretation of 2.5 in this context?
Correct answer: A
In a linear model the slope is the change in y for each increase of 1 in x, so 2.5 is the predicted score increase per extra hour. The predicted score for 0 hours is the y-intercept, 62.
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Question 7
A bag contains 5 red, 3 blue and 2 green marbles. Two marbles are drawn at random, one after the other, without replacement. What is the probability that both marbles are red?
Correct answer: C
The first draw is red with probability 5/10, and then 4 of the remaining 9 marbles are red, so the probability is 5/10 × 4/9 = 20/90 = 2/9. The choice 1/4 = (5/10)² treats the draws as if the first marble were put back.
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Question 8
The table shows the scores of 20 students on a 4-point task.
Score 1 2 3 4 Number of students 3 5 8 4 What is the median score?
Correct answer: D
With 20 scores, the median is the average of the 10th and 11th values. Scores 1 and 2 account for the first 8 students, so the 10th and 11th values are both 3. The choice 2.65 is the mean.
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Question 9
A data set of 9 numbers has a mean of 20. When a tenth number is added, the mean of the 10 numbers becomes 22. What is the tenth number?
Correct answer: C
The original sum is 9 × 20 = 180, and the new sum is 10 × 22 = 220, so the added number is 220 − 180 = 40. The choice 22 is the new mean, not the new value.
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Question 10
A factory produced 6,000 light bulbs in one day. Inspectors tested a random sample of 150 of these bulbs and found 4 defective bulbs. Based on the sample, which is the best estimate of the number of defective bulbs produced that day?
Correct answer: D
The sample defect rate is 4/150, and 4/150 × 6,000 = 160. The choice 40 comes from dividing 6,000 by 150, which gives the number of samples of that size, not the defect count.
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