Introduction

Measures of Spread is an important Grade 6 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with measures of spread.

What Is Measures of Spread?

Measures of Spread means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Measures of Spread

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: The data set \(8, 12, 5, 19, 11, 6, 20\) is displayed on a number line. What is the range?

Visual Model 1

  • A. \(5\)
  • B. \(12\)
  • C. \(15\)
  • D. \(20\)

Why it works: Maximum is \(20\), minimum is \(5\). Range \(= 20 - 5 = 15\).

Answer: \(15\)

Visual Model 2

Question: A dot plot shows the data: one dot at 1, two dots at 3, one dot at 5, one dot at 7, one dot at 9. What is the range?

Visual Model 2

  • A. \(6\)
  • B. \(8\)
  • C. \(2\)
  • D. \(5\)

Why it works: The data set is \(1, 3, 3, 5, 7, 9\). Maximum \(= 9\), minimum \(= 1\). Range \(= 9 - 1 = 8\).

Answer: \(8\)

Worked Examples

Example 1

Question: A box plot shows Q1 \(= 1.5\), median \(= 5\), and Q3 \(= 8.5\). What is the IQR?

Example 1

  • A. \(5\)
  • B. \(6.5\)
  • C. \(7\)
  • D. \(3.5\)
  1. IQR \(= Q3 - Q1 = 8.5 - 1.5 = 7\).

Answer: \(7\)

Example 2

Question: A box plot summary shows min \(= 2\), Q1 \(= 4.5\), median \(= 7.5\), Q3 \(= 10\), max \(= 14\). Find the range and IQR.

Example 2

  • A. Range \(= 12\), IQR \(= 5.5\)
  • B. Range \(= 12\), IQR \(= 3\)
  • C. Range \(= 7.5\), IQR \(= 5.5\)
  • D. Range \(= 5.5\), IQR \(= 2\)
  1. Range \(= \text{max} - \text{min} = 14 - 2 = 12\).
  2. IQR \(= Q3 - Q1 = 10 - 4.5 = 5.5\).

Answer: Range \(= 12\), IQR \(= 5.5\)

Example 3

Question: What is the range of the data set \(15, 22, 9, 30, 18\)?

  • A. \(21\)
  • B. \(18\)
  • C. \(9\)
  • D. \(30\)
  1. Range \(=\) maximum \(-\) minimum \(=30-9=21\).

Answer: \(21\)

Real-World Word Problems

Problem 1

Question: A farmer records the heights of \(6\) plants: \(12, 15, 13, 14, 16, 18\) inches. What is the range of the plant heights?

  • A. \(3\)
  • B. \(5\)
  • C. \(6\)
  • D. \(18\)

Why it works: Maximum \(= 18\), minimum \(= 12\). Range \(= 18 - 12 = 6\) inches.

Answer: \(6\) inches

Problem 2

Question: A teacher records student test scores: \(75, 80, 82, 78, 85\). What is the range?

  • A. \(5\)
  • B. \(7\)
  • C. \(10\)
  • D. \(82\)

Why it works: Maximum \(= 85\), minimum \(= 75\). Range \(= 85 - 75 = 10\).

Answer: \(10\)

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

For the data set \(3, 7, 4, 9, 2, 8, 5\), arrange in order: \(2, 3, 4, 5, 7, 8, 9\). The median is \(5\) and the upper quartile is \(8\). What is the lower quartile?

  • A. \(2\)
  • B. \(5\)
  • C. \(4\)
  • D. \(3\)

Question 2

A data set has minimum value \(12\), Q1 \(= 18\), median \(= 25\), Q3 \(= 32\), and maximum value \(40\). What is the interquartile range?

  • A. \(7\)
  • B. \(14\)
  • C. \(28\)
  • D. \(32\)

Question 3

Using the ordered data \(10, 14, 16, 22, 24, 26, 30, 35\), find Q1 and Q3, then compute the interquartile range.

  • A. \(6\)
  • B. \(12\)
  • C. \(13\)
  • D. \(25\)

Question 4

A box plot of test scores shows Q1 \(= 72\), median \(= 80\), and Q3 \(= 88\). Which value represents the interquartile range?

  • A. \(8\)
  • B. \(16\)
  • C. \(20\)
  • D. \(88\)

Question 5

Two data sets have the same mean of \(50\) but different spreads. Set A has a range of \(12\) and Set B has a range of \(30\). What does this tell you?

  • A. Set A has more variation than Set B.
  • B. The range cannot be compared between sets.
  • C. Both sets have identical variation.
  • D. Set B has more variation than Set A.

Question 6

The mean absolute deviation (MAD) of a data set is the average distance of each data point from the mean. For the data \(5, 7, 9\), the mean is \(7\). The distances are \(|5-7| = 2\), \(|7-7| = 0\), \(|9-7| = 2\). What is the MAD?

  • A. \(0\)
  • B. \(\frac{4}{3}\)
  • C. \(2\)
  • D. \(4\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \(3\)

The lower half of the ordered data is \(2, 3, 4\). The median of the lower half (lower quartile, Q1) is \(3\).

Question 2

Answer: \(14\)

IQR \(= Q3 - Q1 = 32 - 18 = 14\). This measures the spread of the middle \(50\%\) of the data.

Question 3

Answer: \(13\)

Split the ordered data into two halves. The lower half is \(10,14,16,22\), so \(Q1=\frac{14+16}{2}=15\). The upper half is \(24,26,30,35\), so \(Q3=\frac{26+30}{2}=28\). The IQR is \(28-15=13\).

Question 4

Answer: \(16\)

IQR \(= Q3 - Q1 = 88 - 72 = 16\). The IQR tells us the spread of the middle half of the scores.

Question 5

Answer: Set B has more variation.

A larger range indicates greater spread. Set B's range of \(30\) is larger than Set A's range of \(12\), so Set B has more variability.

Question 6

Answer: \(\frac{4}{3}\) or approximately \(1.33\)

MAD \(= \frac{2 + 0 + 2}{3} = \frac{4}{3} \approx 1.33\). The MAD shows how spread out the data is on average.

Timed practice quizzes

Related Quizzes

After studying Measures of Spread, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 6 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Measures of Spread becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.