Praxis Core Math Data Interpretation and Representation, Statistics, and Probability

Content category II of the Core Academic Skills for Educators: Mathematics (5733): about 18 of the 56 questions (32%). The topics ETS lists, how they are tested and practice questions with explanations.

Take a full timed Praxis Core Math practice test

56 questions on the real 90-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.

Or start the free Data Interpretation and Representation, Statistics, and Probability drill

What ETS lists

  • Working with data and data representations to solve problems
  • Measures of central tendency (mean, median) and spread (range, standard deviation)
  • Drawing inferences about a population from a random sample
  • Positive and negative linear relationships in scatterplots
  • Using a linear model for a data set to make predictions
  • Correlation versus causation
  • Simple probabilities

From the ETS Core Academic Skills for Educators: Mathematics (5733) Study Companion, content category II.

Line drawing of a scatter plot on graph paper, a pair of dice and a spinner

How Data Interpretation and Representation, Statistics, and Probability is tested

Reading tables, bar graphs, line graphs, circle graphs and scatterplots; computing mean, median, mode and range; reasoning about samples; using a trend line to predict; telling correlation from causation; and simple probability. The arithmetic is light; careful reading wins the points.

Start the free Data Interpretation and Representation, Statistics, and Probability drill

Praxis Core Math Data Interpretation and Representation, Statistics, and Probability practice questions

Answer each question, then open the explanation.

Question 1

A scatterplot compares weekly practice hours with performance scores. The points cluster around a line rising from lower left to upper right. What relationship does the plot show?

  1. A.A positive linear association
  2. B.A negative linear association
  3. C.A constant performance score
  4. D.A circular association
  5. E.No association
Show the answer and explanation

Answer: A: A positive linear association

A line rising from left to right indicates that larger practice-hour values tend to accompany larger scores. Clustering around a line makes the association linear.

Question 2

A set of four numbers has a mean of 18. Three of the numbers are 12, 17, and 25. What is the fourth number? Enter your answer as a whole number.

Numeric entry.

Show the answer and explanation

Answer: 18

The four numbers must sum to 4 × 18 = 72. The known numbers sum to 54, leaving 72 − 54 = 18.

Question 3

A fitted line passes through the points (2, 9) and (6, 19). At x = 8, the observed value of y is 29. Using residual = observed − predicted, what is the residual?

  1. A.-5
  2. B.5
  3. C.24
  4. D.29
  5. E.53
Show the answer and explanation

Answer: B: 5

The fitted slope is (19 − 9)/(6 − 2) = 2.5, so at x = 8 the line predicts 9 + 2.5(8 − 2) = 24. The residual is 29 − 24 = 5; reversing the subtraction gives the wrong sign.

Question 4

A histogram groups commute times into intervals of 0 to under 10, 10 to under 20, 20 to under 30, and 30 to under 40 minutes. The bar heights are 3, 8, 11, and 4, respectively. Which interval contains the greatest number of commutes?

  1. A.All four intervals have equal counts
  2. B.0 to under 10 minutes
  3. C.10 to under 20 minutes
  4. D.20 to under 30 minutes
  5. E.30 to under 40 minutes
Show the answer and explanation

Answer: D: 20 to under 30 minutes

The tallest bar has height 11 and represents times from 20 to under 30 minutes. A higher time interval does not necessarily have a greater frequency.

Take the full test under the real clock

Take a full timed Praxis Core Math practice test

56 questions on the real 90-minute clock, weighted like the ETS test, with a score by content category and an explanation for every answer.

Or start the free Data Interpretation and Representation, Statistics, and Probability drill

Common questions

How many Data Interpretation and Representation, Statistics, and Probability questions are on the Praxis Core Math?

ETS lists about 18 of the 56 questions in Data Interpretation and Representation, Statistics, and Probability, about 32% of the test.

What does Data Interpretation and Representation, Statistics, and Probability cover on the Praxis Core Math?

Working with data and data representations to solve problems; Measures of central tendency (mean, median) and spread (range, standard deviation); Drawing inferences about a population from a random sample; Positive and negative linear relationships in scatterplots; Using a linear model for a data set to make predictions; Correlation versus causation; Simple probabilities.

How should I study Data Interpretation and Representation, Statistics, and Probability for the Praxis Core Math?

Reading tables, bar graphs, line graphs, circle graphs and scatterplots; computing mean, median, mode and range; reasoning about samples; using a trend line to predict; telling correlation from causation; and simple probability. The arithmetic is light; careful reading wins the points.

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