Unit 6 · Topic 2

Spread: Range & IQR

Overview

Two ways to measure how spread out a data set is.

Topic 2 of 3~45 min
Unit overview

The lesson

This lesson teaches Spread: Range & IQR. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Range

Range is the simplest measure of spread: the largest value minus the smallest value. It's quick, but a single extreme value can stretch it a lot.

When you study range, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

Worked example

Find the range of 2, 5, 7, 8, 11, 14, 20.

  1. 1Largest − smallest.
  2. 220 − 2 = 18.

Interquartile range (IQR)

IQR measures the spread of the middle 50% of the data. Because it ignores the extreme high and low values, it is less affected by outliers than the range.

When you study interquartile range (iqr), slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

Why this matters

Spread: Range & IQR shows up constantly in two ways to measure how spread out a data set is. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

  1. Range
  2. Interquartile range (IQR)

Video walkthrough

Khan Academy

Range and Interquartile Range

Compare the full spread vs. the middle 50%.

Watch on YouTube
Math with Mr. J

Interquartile Range (IQR)

Measure the spread of the middle half of your data.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Find the range of: 15, 22, 18, 30, 12.

Step-by-step solution

  1. 1Maximum − minimum = 30 − 12.
  2. 2Range = 18.

Exercise 2

Try it yourself

Data set: 4, 8, 10, 12, 16, 20. Find the range.

Step-by-step solution

  1. 120 − 4 = 16.

Exercise 3

Try it yourself

For the data 3, 5, 7, 9, 11, 13, 15, the median is 9. What percent of the data lies between the minimum and median?

Step-by-step solution

  1. 1Values below 9: 3, 5, 7 → 3 out of 7 values.
  2. 2About 3/7 of the data is below the median (roughly the lower half).

Exercise 4

Try it yourself

Two data sets both have range 20. Set A: 10–30. Set B: 0–20 with one value 50. Which range is more misleading?

Step-by-step solution

  1. 1Set B has an outlier at 50 that stretches the range.
  2. 2IQR would describe Set B's middle better than range.

Exercise 5

Try it yourself

A data set has Q1 = 12, Q3 = 20. Find the IQR.

Step-by-step solution

  1. 1IQR = Q3 − Q1.
  2. 2IQR = 20 − 12 = 8.

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Spread: Range & IQR

Question 1 of 5

Easy

Find the range of 2, 5, 7, 8, 11, 14, 20.

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