Grade 6 Dot Plots and Histograms

Introduction

Dot Plots and Histograms 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 dot plots and histograms.

What Is Dot Plots and Histograms?

Dot Plots and Histograms means reading, creating, and explaining displays so data can answer real questions.

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 Dot Plots and Histograms

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

Read the title, labels, and scale before answering.
Use the scale value instead of counting marks as ones when the graph is scaled.
Compare categories by subtracting or adding values from the display.
Explain what the data shows in a complete sentence.

Visual Models

Visual Model 1

Question: The dot plot shows the number of books read by students last month. How many students read exactly \(3\) books?

Visual Model 1

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

Why it works: Count the dots above the number \(3\): there are \(4\) dots, so \(4\) students read exactly \(3\) books.

Answer: \(4\)

Visual Model 2

Question: A dot plot displays the ages of people visiting an ice cream shop. The dot plot shows \(5\) people aged \(9\) years old, \(8\) people aged \(12\) years old, and \(3\) people aged \(15\) years old. How many total people are represented in the dot plot?

Visual Model 2

A. \(16\)
B. \(25\)
C. \(20\)
D. \(18\)

Why it works: Add the number of people at each age: \(5 + 8 + 3 = 16\) total people.

Answer: \(16\)

Worked Examples

Example 1

Question: The dot plot below shows the number of hours sixth graders spent doing homework in one week. What is the mode (most common value) of the data?

Example 1

A. \(6\) hours
B. \(3\) hours
C. \(4\) hours
D. \(7\) hours

Count the dots stacked above each value.
The tallest stack is at \(6\) hours with \(5\) dots, which is more than at any other value, so \(6\) hours is the mode.

Answer: \(6\) hours

Example 2

Question: A histogram shows the test scores for a class of 30 students, grouped into ranges. The bars show: \(0\)--\(10\) has height \(2\), \(11\)--\(20\) has height \(5\), \(21\)--\(30\) has height \(8\), and \(31\)--\(40\) has height \(15\). How many students scored between \(21\) and \(30\)?

Example 2

A. \(5\) students
B. \(8\) students
C. \(15\) students
D. \(10\) students

The bar for the \(21\)--\(30\) range has a height of \(8\), which represents the frequency (number of students) in that range.

Answer: \(8\) students

Example 3

Question: A dot plot shows the number of pencils in each student's pencil case. Which statement is true about the data?

Example 3

A. Most students have \(4\) pencils
B. Most students have \(6\) pencils
C. Most students have \(8\) pencils
D. No students have \(7\) pencils

The value \(6\) has the most dots (\(5\)), making it the mode.
The other statements are false: only \(2\) have \(4\) pencils, and there are \(2\) with \(7\) pencils.

Answer: Most students have \(6\) pencils

Real-World Word Problems

Problem 1

Question: The histogram below shows the height (in inches) of tomato plants after \(4\) weeks. How many plants are between \(18\) and \(24\) inches tall?

Problem 1

A. \(6\) plants
B. \(20\) plants
C. \(12\) plants
D. \(14\) plants

Why it works: The bar for the \(18\)--\(24\) inch range has a height of \(14\), representing the number of plants in that height range.

Answer: \(14\) plants

Problem 2

Question: The histogram shows the number of hours per week teenagers spend on social media. How many teenagers spend between \(5\) and \(15\) hours per week?

Problem 2

A. \(16\) teenagers
B. \(34\) teenagers
C. \(42\) teenagers
D. \(50\) teenagers

Why it works: Add the frequencies for the \(5\)--\(10\) and \(10\)--\(15\) ranges: \(16 + 18 = 34\) teenagers.

Answer: \(34\) teenagers

Common Mistakes

Ignoring the graph scale.
Reading the wrong category or axis label.
Answering a comparison question without subtracting.
Writing a number without explaining what it represents.

Strategy Tips

Circle the scale before using the graph.
Write down the value for each category you compare.
Use addition for totals and subtraction for differences.
Answer in words so the data result has meaning.

Practice Questions

Question 1

A dot plot shows the number of goals scored by different soccer teams during a season. If the dot plot shows \(3\) teams scored \(5\) goals, \(2\) teams scored \(6\) goals, \(4\) teams scored \(7\) goals, and \(1\) team scored \(8\) goals, what is the total number of goals scored by all teams combined?

Question 1

A. \(63\) goals
B. \(50\) goals
C. \(75\) goals
D. \(60\) goals

Question 2

Which histogram correctly represents a data set where the frequency is highest for the \(20\)--\(30\) range and lowest for the \(50\)--\(60\) range?

Question 2

A. This histogram is correct
B. The \(20\)--\(30\) range is too low
C. The \(50\)--\(60\) range is too high
D. The bars are not properly ordered

Question 3

A dot plot displays the test scores: \(70, 75, 75, 80, 80, 80, 85, 90\). What is the median score?

Question 3

A. \(75\)
B. \(80\)
C. \(85\)
D. \(77.5\)

Question 4

A dot plot shows the number of siblings each student has. The distribution is: \(0\) siblings: \(2\) students; \(1\) sibling: \(5\) students; \(2\) siblings: \(6\) students; \(3\) siblings: \(4\) students; \(4\) siblings: \(3\) students. Which best describes the shape of this distribution?

Question 4

A. Symmetric
B. Skewed right
C. Skewed left
D. Bimodal

Question 5

The histogram below shows a data distribution. Which statement is accurate?

Question 5

A. The distribution is skewed left
B. The distribution is bimodal
C. The distribution is symmetric
D. The distribution is skewed right