How to Interpret Histogram? (+FREE Worksheet!)

Imagine sorting your class by height into a few buckets, then stacking the buckets so you can see how tall each pile is. That picture is a histogram: a bar chart where each bar shows how many values fall inside a numeric range, called a bin. The bars touch (no gaps), because the data is continuous. Read a histogram and you can spot the shape, the center, the spread, and any sneaky outliers your data is hiding.

Key takeaways:

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Histograms show frequency of values in numerical bins (intervals).
Bars touch - unlike a bar graph, where categorical bars have gaps.
The x-axis shows the bins; the y-axis shows the frequency or count.
Look at shape (symmetric, skewed, bimodal), center, and spread.
A histogram of test scores in bins of width 10 shows how many students fell in each range.

Histograms represent the distribution of numerical data. Learn how to interpret and solve Math problems containing histograms. For education statistics and research

How to Interpret Histogram? (+FREE Worksheet!)

Tutor-style math help

Data Displays, Stem-and-Leaf Plots, and Circle Graphs: what to notice and how to work it

Statistics skill

Data displays organize values so patterns are easier to see. Histograms show intervals, stem-and-leaf plots keep exact values, and circle graphs show parts of a whole.

What to notice first

Match the display to the question. Use a histogram for shape, a stem-and-leaf plot for ordered exact data, and a circle graph for percent shares.

Common student mistake

Do not read a histogram bar as one exact value. Each bar represents a whole interval.

Key formulas and cues

\(\text{relative frequency}=\frac{\text{category count}}{\text{total count}}\)

\(\text{circle graph angle}=360^\circ\cdot\text{part fraction}\)

\(\text{histogram bars touch}\)

A reliable path

Identify the questionDecide whether you need center, spread, shape, or association.
Use the right displayChoose a histogram, box plot, scatter plot, or summary statistic.
Write the meaningExplain what the statistic says about the data set.

Worked examples

Read a histogram interval

Example: The 10-19 bar has height 7.

The interval is 10 through 19.
Height tells how many data values fall there.
There are 7 values in that interval.

Answer: 7 values

Circle graph percent

Example: A category is 1/4 of the data.

Circle graphs use the full circle as 100%.
1/4 is 25%.
The angle is 1/4 of 360 degrees.

Answer: 25%, or 90 degrees.

Open pop-up practice

Try one before moving on

Try: A category is 30 out of 120. What percent is it?

Answer: 25%.

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

Watch this practice video for additional examples and reinforcement:

What’s a Histogram?

Histograms are the graphical interpretation of information where information is grouped into constant amount ranges and each of those ranges relates to a vertical bar.

A horizontal axis shows the number range.
A vertical axis (frequency) signifies the quantity of information available for each range.

The number ranges are dependent upon the information being utilized. So, here’s more info regarding histograms.

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The method of creating histograms utilizing the provided info is shown here:

Step one: Pick an appropriate scale to designate weights on a horizontal axis.
Step two: Pick an appropriate scale to designate the frequencies on a vertical axis.
Step three: After that, make the bars consistent with each of these given weights by utilizing their occurrences.

Hints and Techniques on Histograms

Here are several vital hints and techniques you should remember while envisioning any information via histograms.

Pick the scale for the vertical axis whilst creating a histogram, make sure to check for the uppermost number that separates all frequencies. If there’s no such number existing, after that check for the utmost number which separates the majority of frequencies.
Histograms are graphs utilized to summarize constant information.
A histogram gives the visual interpretation of continuous data.
Scales of both the horizontal and vertical axes do not have to begin with zero.
There ought not to be any gaps between the bars of histograms.
To interpret histograms, check the height of each bar that shows how many fall into each range.

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Histogram Example: Reading Equal-Width Bins

A class records how many minutes 20 students spend reading. The histogram groups the times into four intervals. Each interval includes its lower endpoint but not its upper endpoint.

Reading time for 20 students
Minutes	Frequency
0 to less than 10	3
10 to less than 20	7
20 to less than 30	6
30 to less than 40	4

Worked example: The tallest bar is the 10-to-less-than-20-minute interval, with 7 students. The total is 3 + 7 + 6 + 4 = 20 students. Students who read for at least 20 minutes number 6 + 4 = 10, or 50% of the class.

Practice

How many students read for less than 20 minutes?
Which interval has the smallest frequency?
Can the histogram tell you the exact reading time of every student?

Answers and explanations

10 students: add the first two frequencies, 3 + 7.
0 to less than 10 minutes, with 3 students.
No. A histogram shows grouped frequencies, not every individual value.

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Frequently Asked Questions

What are histograms used for?

Histograms are used to show how numerical data is distributed, meaning how many values fall into each range. They make it easy to see where most values cluster and whether the data is spread out. For example, a histogram of test scores in bins of 60–69, 70–79, and 80–89 shows at a glance which score band had the most students.

What is the difference between a histogram and a bar graph?

A histogram shows numerical data grouped into intervals, so its bars touch. A bar graph compares separate categories, such as favorite fruits, so its bars have gaps between them. Another clue is the x-axis: a histogram’s axis is a number line of ranges like 0–10 and 10–20, while a bar graph’s axis lists category names.

What type of data are histograms used for?

Histograms are used for quantitative data, values you can measure or count on a number line, such as heights, times, or test scores. The data is grouped into equal-width bins. Categorical data, like eye color or favorite sport, belongs in a bar graph or circle graph instead, because those categories have no numerical order.

What does a histogram show?

A histogram shows the shape, center, and spread of a data set. Look for whether it is symmetric, skewed right (a long tail toward higher values), skewed left, or has two peaks. Also notice gaps and outliers. Remember that each bar is a whole interval: a bar of height 6 over 20–30 means six values somewhere in that range, not six values of 25.

How do you make a histogram on a TI-84?

Press STAT, choose Edit, and type your data into L1. Then press 2nd and Y= for STAT PLOT, open Plot1, turn it On, and pick the histogram icon with Xlist set to L1 and Freq set to 1. Press ZOOM and choose 9 (ZoomStat) to draw it. You can change the bin width with Xscl in the WINDOW menu.

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How to Interpret Histogram? (+FREE Worksheet!)