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Question 1
StatisticsFoundation

Statistics practice question 1

Statistics practice topics

Question sets mix direct skills with unfamiliar applications so method selection becomes part of the practice.

01

Data summaries and displays

Calculate mean, median, spread, and quartiles, and work backwards from a summary to a missing data value.

02

Probability and random variables

Count favorable outcomes, combine events with the addition and multiplication rules, and compute expected values.

03

Sampling distributions and inference

Find the standard error of a mean or proportion, and read the point estimate and margin of error out of a confidence interval.

04

Correlation and regression

Interpret the correlation coefficient, use a regression line to predict, and find the intercept from the point of means.

Statistics practice questions with worked answers

These 8 questions are printed in full on this page, with every step of the arithmetic written out. Cover the options, solve the question on paper first, and only then open the worked answer to compare your method with the one shown.

Question 1: Find the median of 4, 9, 2, 7, 12, 5.

Foundation level · data summaries and displays

  1. 6
  2. 6.5
  3. 7
  4. 5
Show the worked answer
  1. Put the values in order: 2, 4, 5, 7, 9, 12.
  2. There are 6 values, an even count, so the median is the average of the middle two.
  3. The middle two values are 5 and 7.
  4. (5 + 7)/2 = 6, so the median is 6.

Answer: 6

Question 2: Five test scores have a mean of 20. A sixth score of 32 is added. What is the new mean?

Exam level · data summaries and displays

  1. 22
  2. 26
  3. 24
  4. 21
Show the worked answer
  1. Mean x count gives the total, so the first five scores add to 20 x 5 = 100.
  2. Adding the sixth score gives a new total of 100 + 32 = 132.
  3. There are now 6 scores.
  4. 132 / 6 = 22, so the new mean is 22.

Answer: 22

Question 3: Two fair six-sided dice are rolled. What is the probability that the two numbers add to 7?

Foundation level · probability and random variables

  1. 1/6
  2. 1/12
  3. 7/36
  4. 1/9
Show the worked answer
  1. Each die has 6 faces, so there are 6 x 6 = 36 equally likely outcomes.
  2. The pairs that add to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).
  3. That is 6 winning outcomes out of 36.
  4. 6/36 simplifies to 1/6, which is about 0.167.

Answer: 1/6

Question 4: A spinner pays $5 with probability 0.3, pays $2 with probability 0.5, and pays nothing otherwise. What is the expected payout for one spin?

Exam level · probability and random variables

  1. $2.50
  2. $3.50
  3. $2.00
  4. $7.00
Show the worked answer
  1. Expected value multiplies each payout by its probability, then adds the results.
  2. The $5 outcome contributes 5 x 0.3 = 1.50.
  3. The $2 outcome contributes 2 x 0.5 = 1.00, and the $0 outcome contributes 0.
  4. 1.50 + 1.00 + 0 = 2.50, so the expected payout is $2.50 per spin.

Answer: $2.50

Question 5: A population has a standard deviation of 15. A random sample of 25 is taken. What is the standard deviation of the sample mean?

Exam level · sampling distributions and inference

  1. 3
  2. 0.6
  3. 15
  4. 5
Show the worked answer
  1. The standard deviation of the sample mean is the population standard deviation divided by the square root of the sample size.
  2. The square root of 25 is 5.
  3. 15 / 5 = 3.
  4. So sample means vary with a standard deviation of 3, which is much less spread than the raw data.

Answer: 3

Question 6: A 95% confidence interval for a population mean runs from 48 to 56. What are the point estimate and the margin of error?

Challenge level · sampling distributions and inference

  1. Point estimate 52, margin of error 4
  2. Point estimate 52, margin of error 8
  3. Point estimate 48, margin of error 8
  4. Point estimate 56, margin of error 4
Show the worked answer
  1. A confidence interval is the point estimate plus or minus the margin of error, so the estimate sits in the middle.
  2. Point estimate = (48 + 56)/2 = 104/2 = 52.
  3. The full width is 56 - 48 = 8, and the margin of error is half of that.
  4. 8/2 = 4, so the interval is 52 plus or minus 4.

Answer: Point estimate 52, margin of error 4

Question 7: A regression line is y-hat = 3.5x + 12. What value does it predict when x = 8?

Foundation level · correlation and regression

  1. 40
  2. 28
  3. 43.5
  4. 36
Show the worked answer
  1. Substitute x = 8 into the equation.
  2. 3.5 x 8 = 28.
  3. Add the intercept: 28 + 12 = 40.
  4. The predicted value is 40. The intercept 12 is the prediction when x = 0.

Answer: 40

Question 8: A regression line has slope 2.4 and passes through the point of means (10, 45). What is the intercept, and what does the line predict at x = 15?

Challenge level · correlation and regression

  1. Intercept 21, prediction 57
  2. Intercept 21, prediction 36
  3. Intercept 45, prediction 81
  4. Intercept 35, prediction 71
Show the worked answer
  1. Every least-squares line passes through the point of means, so 45 = 2.4(10) + b.
  2. 2.4 x 10 = 24, so 45 = 24 + b and b = 21.
  3. The line is y-hat = 2.4x + 21.
  4. At x = 15: 2.4 x 15 = 36, and 36 + 21 = 57.

Answer: Intercept 21, prediction 57

How the three Statistics difficulty levels differ

The difficulty buttons above change what a question asks of you, not just the size of the numbers. Each example below is taken from the question set on this page.

Difficulty levels for Statistics practice, with an example question from this page.
LevelWhat it testsExample questionTime target
FoundationOne skill at a time, with the numbers kept small enough to check in your head.Find the median of 4, 9, 2, 7, 12, 5.About 1 minute
ExamThe wording of a real test paper: pick the method first, then carry out two or three steps.Five test scores have a mean of 20. A sixth score of 32 is added. What is the new mean?2 to 3 minutes
ChallengeTwo ideas combined, or a result you have to interpret after the calculation ends.A 95% confidence interval for a population mean runs from 48 to 56. What are the point estimate and the margin of error?4 to 5 minutes

How to practice Statistics effectively

Begin without notes and explain your choice before checking. For every miss, identify whether the cause was a definition, setup, calculation, interpretation, or time decision. Re-solve the question from a blank page, then return to the same skill in a mixed set tomorrow.

What your Statistics answer review should show

A useful review shows more than the correct option. Compare the method with your first attempt, locate the earliest incorrect decision, and write one rule that would prevent the same error in a new Statistics problem.

Move from mixed Statistics questions to a complete course

This page targets flexible Statistics question practice. When you need a syllabus-aligned sequence with unit selection, use Probability and Statistics practice by unit and return here later for mixed retrieval.

Questions about Statistics practice

When should I change the difficulty?

Move up after you can solve several questions accurately without hints and explain the method. Move down for one short set when errors show that a definition or setup is still uncertain.

How often should I practice?

Short sessions on several days usually build stronger recall than one long session. Revisit missed Statistics skills the next day, then mix them with older topics later in the week.

Where can I review the lessons in order?

Use Probability and Statistics practice by unit for a syllabus-aligned sequence with unit selection, practice, and a complete answer review.

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