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Praxis Core · Mathematics (5733)

Praxis Core: Data Interpretation, Statistics, and Probability Concepts

Importance ★★★★★ · 32% (estimate)

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Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.

Overview

This chapter is the second-largest part of the Math test. You will read tables and graphs, find the mean, median, mode, and range of a data set, and work out simple probabilities.

Reading data starts with the labels: check the title, the axes, the scale, and the units. Then the measures of center describe a typical value. The mean is the average, the median is the middle after ordering, and the mode is the most frequent value. The range shows the spread.

Outliers are values far from the rest. They pull the mean much more than the median, so the median often describes skewed data better. Probability is the number of favorable outcomes divided by the number of equally likely outcomes, giving a value from 0 to 1.

Key concepts

  • Mean

    The average: add all the values, then divide by how many values there are.

    Memory tipSum ÷ count.

  • Median

    The middle value after putting the data in order. If there is an even number of values, the median is the mean of the two middle values.

    Memory tipOrder first, then find the middle.

  • Mode and range

    The mode is the value that appears most often; a set can have no mode or more than one. The range is the largest value minus the smallest value.

    Memory tipMode = most. Range = max − min.

  • Outlier

    A value much higher or lower than the rest of the data. Outliers change the mean much more than the median or mode.

    Memory tipOne giant salary raises the average but barely moves the middle.

  • Simple probability

    P(event) = number of favorable outcomes ÷ total number of equally likely outcomes. Probability is between 0 (impossible) and 1 (certain).

    Memory tipWhat you want ÷ everything that can happen.

  • Independent events

    When one event does not affect the other, the probability that both happen is P(A) × P(B). Example: two coin flips both heads = ½ × ½ = ¼.

    Memory tip"And" with independent events means multiply.

  • Reading graphs

    Check the title, axis labels, scale, and units before reading values. Bar graphs compare categories, line graphs show change over time, and circle graphs show parts of a whole.

    Memory tipWatch the scale: it may not start at zero or count by ones.

Often tested

  • The median is the middle value after the data are put in order.
  • An outlier changes the mean much more than the median.
  • Probability = favorable outcomes divided by all equally likely outcomes.
  • Range is the largest value minus the smallest value.
  • Check a graph's scale before reading values from it.

Easy to confuse: Mean vs. median vs. mode

MeasureHow to find itEffect of an outlier
MeanAdd all values, divide by the countPulled strongly
MedianMiddle value after orderingLittle effect
ModeMost frequent valueUsually no effect

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedMathematics (5733) › Data Interpretation, Statistics, and Probability★★★★★

Question 1. Find the mean of these numbers: 10, 15, 9, 22, 16

  1. ① 15
  2. ② 18
  3. ③ 13
  4. ④ 72
  5. ⑤ 14.4
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ⑤ 14.4

Key point: Mean = sum of the values ÷ number of values.

  1. Sum: 10 + 15 + 9 + 22 + 16 = 72.
  2. Mean: 72 ÷ 5 = 14.4.

Check: 14.4 × 5 = 72.

Wrong choices

  • "15": 15 is the median (the middle value when ordered), not the mean.
  • "18": This divides the total (72) by 4 instead of by 5 numbers.
  • "13": 13 is the range (22 − 9), not the mean.
  • "72": 72 is the total. It must be divided by how many numbers there are.
Practice questionReviewedMathematics (5733) › Data Interpretation, Statistics, and Probability★★★★★

Question 2. What is the median of 7, 3, 9, 4, 12, 8?

  1. ① 7
  2. ② 7.5
  3. ③ 8
  4. ④ 9
  5. ⑤ 6.5
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ② 7.5

Key point: Order the data; with an even count, average the two middle values.

  1. Order: 3, 4, 7, 8, 9, 12.
  2. The two middle values are 7 and 8.
  3. Median: (7 + 8) ÷ 2 = 7.5.

Check: three values (3, 4, 7) are below 7.5 and three (8, 9, 12) are above it.

Wrong choices

  • "6.5": This takes the middle two numbers without first putting the list in order (9 and 4).
  • "7": With six numbers there are two middle values (7 and 8); the median is their average.
  • "8": This picks only one of the two middle values.
  • "9": 9 is the range (12 − 3), not the median.
Practice questionReviewedMathematics (5733) › Data Interpretation, Statistics, and Probability★★★★★

Question 3. A bag holds 4 red, 6 blue, and 5 green marbles. One marble is picked at random. What is the probability that it is blue?

  1. ① 2/5
  2. ② 2/3
  3. ③ 3/5
  4. ④ 1/3
  5. ⑤ 1/6
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① 2/5

Key point: Probability = favorable outcomes ÷ total outcomes.

  1. Total marbles: 4 + 6 + 5 = 15.
  2. Blue: 6.
  3. Probability: 6/15 = 2/5.

Check: 2/5 = 0.4, and 0.4 × 15 = 6 blue marbles.

Wrong choices

  • "2/3": This compares blue to non-blue (6 to 9). Probability compares blue to ALL marbles (6 out of 15).
  • "3/5": 3/5 is the probability of NOT picking blue.
  • "1/3": This assumes the three colors are equally likely. There are more blue marbles than red or green.
  • "1/6": This puts 1 over the number of blue marbles.
Practice 5 questions from this unit →