Line Plots and Histograms — How to Read and Create Them

By MathPal Editorial Team·Published Apr 17, 2026

Grade: 6-7 | Topic: Statistics

What You Will Learn

Graphs turn raw numbers into pictures you can understand at a glance. In this guide you will learn two important types of data displays: line plots (also called dot plots) for small data sets with individual values, and histograms for larger data sets grouped into ranges. You will also learn how to build a frequency table, choose a good bin width, and interpret what these graphs tell you.

Theory

Line plots (dot plots)

A line plot uses dots (or Xs) stacked above a number line to show how often each value appears. Each dot represents one data point.

When to use a line plot: Line plots work best for small data sets (roughly 10-30 values) where the values are discrete — things like shoe sizes, quiz scores out of 10, or number of siblings.

How to create a line plot:

1. Draw a horizontal number line covering the range of your data.
2. For each data value, place a dot above that number.
3. Stack dots vertically when the same value appears more than once.
4. Add a title and label the number line.

Frequency tables

Before building a histogram, you often organize data into a frequency table. This table lists each category (or range) and counts how many data points fall into it.

Score range	Tally	Frequency
60-69	III	3
70-79	IIII I	6
80-89	IIII IIII	9
90-100	IIII	4

Histograms

A histogram looks similar to a bar chart, but it displays numerical data grouped into intervals (called bins). The bars touch each other because the ranges are continuous — there are no gaps between them.

Key features of a histogram:

• The x-axis shows the intervals (bins).
• The y-axis shows the frequency (count) for each bin.
• The bars touch — no gaps.
• Each bar includes the left endpoint but not the right (for example, the bin 70-80 includes 70 but not 80).

Choosing bin width

The bin width is the size of each interval. To choose it:

1. Find the range: largest value minus smallest value.
2. Decide on a number of bins (5 to 10 is typical).
3. Divide: bin width = range / number of bins.
4. Round to a convenient number.

For example, if test scores range from 52 to 98, the range is 46. With 5 bins: $46 \div 5 = 9.2$, so a bin width of 10 is a nice choice.

Worked Examples

Example 1 — Creating a line plot

A teacher recorded the number of books 12 students read last month: 2, 3, 1, 4, 3, 2, 5, 3, 2, 1, 3, 4.

Step 1: The values range from 1 to 5. Draw a number line from 1 to 5.

Step 2: Count each value:

• 1 appears 2 times
• 2 appears 3 times
• 3 appears 4 times
• 4 appears 2 times
• 5 appears 1 time

Step 3: Stack dots above each number accordingly.

Interpretation: The most common number of books read is 3 (the tallest stack). Most students read 2-4 books.

Example 2 — Reading a histogram

A histogram shows student heights in centimeters with these bins and frequencies: 140-145 (2 students), 145-150 (5 students), 150-155 (8 students), 155-160 (6 students), 160-165 (3 students).

Questions and answers:

• How many students total? $2 + 5 + 8 + 6 + 3 = 24$ students.
• Which height range is most common? 150-155 cm (the tallest bar, 8 students).
• How many students are shorter than 150 cm? $2 + 5 = 7$ students.

Example 3 — Building a histogram from raw data

Here are the ages of 20 people at a community event: 8, 12, 15, 22, 25, 27, 30, 31, 33, 35, 38, 40, 42, 45, 48, 50, 55, 60, 62, 70.

Step 1: Range = $70 - 8 = 62$. Choose bin width of 10 with bins starting at 0.

Step 2: Build the frequency table:

Age range	Frequency
0-9	1
10-19	2
20-29	3
30-39	5
40-49	4
50-59	2
60-69	2
70-79	1

Step 3: Draw the histogram — 8 bars, tallest at 30-39.

Interpretation: The event attracted mainly adults in their 30s and 40s, with fewer children and seniors.

Example 4 — Comparing bin widths

Using the same age data, what happens if we use a bin width of 20 instead of 10?

Age range	Frequency
0-19	3
20-39	8
40-59	6
60-79	3

The histogram now has only 4 bars. It still shows the general shape (most people aged 20-59), but we lose the detail that 30-39 was the peak group. Smaller bins give more detail; larger bins give a smoother, simpler picture.

Common Mistakes

Mistake 1 — Leaving gaps in a histogram

❌ Drawing spaces between histogram bars like a bar chart.

✅ Histogram bars must touch because the data ranges are continuous. A gap would imply values that belong to no bin.

Mistake 2 — Using unequal bin widths without adjusting

❌ Making one bin 60-70 and the next 70-100, then comparing their bar heights directly.

✅ Either keep all bins the same width, or use frequency density (frequency divided by bin width) on the y-axis for unequal bins.

Mistake 3 — Confusing histograms with bar charts

❌ Using a histogram for categorical data like "favorite color."

✅ Histograms are for numerical data grouped into ranges. Use a bar chart for categories, where bars do not touch.

Practice Problems

Problem 1: A class recorded daily temperatures (in degrees F) for a week: 72, 75, 68, 74, 71, 73, 76. Create a line plot. What is the most frequent temperature?

Show Answer

Each temperature appears exactly once, so no value is more frequent than another. The line plot has one dot above each value: 68, 71, 72, 73, 74, 75, 76.

Problem 2: A histogram has bins 0-10, 10-20, 20-30, 30-40 with frequencies 5, 12, 8, 3. How many data points are there in total?

Show Answer

$5 + 12 + 8 + 3 = 28$ data points.

Problem 3: Data ranges from 15 to 85. Suggest a reasonable bin width if you want about 7 bins.

Show Answer

Range $= 85 - 15 = 70$. Bin width $= 70 \div 7 = 10$. A bin width of 10 works perfectly.

Problem 4: From this frequency table, which interval has the highest frequency?

Interval	Frequency
0-4	3
5-9	7
10-14	11
15-19	5

Show Answer

The interval 10-14 has the highest frequency at 11.

Problem 5: True or false: A histogram and a bar chart are the same thing.

Show Answer

False. A histogram displays numerical data in continuous ranges (bars touch), while a bar chart displays categorical data (bars are separated by gaps).

Summary

• A line plot (dot plot) shows individual data values as dots above a number line — best for small, discrete data sets.
• A histogram groups numerical data into bins and shows frequency with touching bars — best for larger or continuous data.
• Always build a frequency table before drawing a histogram.
• Bin width affects the level of detail: smaller bins reveal more patterns, larger bins simplify the picture.
• Histograms and bar charts look similar but serve different purposes — histograms are for numerical ranges, bar charts for categories.

Related Topics

• Statistics Basics — mean, median, mode, and range
• Reading Bar Charts and Pie Charts — categorical data displays
• Data Collection and Analysis — designing surveys and organizing data

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