How to Interpret Histogram? (+FREE Worksheet!)

Watch this practice video for additional examples and reinforcement:

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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.

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

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

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Frequently Asked Questions

What is a histogram?

A histogram is a chart that shows how often values fall into specific numerical intervals, called bins. The horizontal axis shows the bins (like 60-69, 70-79, 80-89, 90-99 for test scores), and the vertical axis shows the count or frequency of values in each bin. Bars touch each other because the underlying data is continuous – there’s no “gap” between consecutive bins.

How is a histogram different from a bar graph?

A bar graph compares separate categories (favorite color, sport, brand), so its bars have gaps between them. A histogram shows the distribution of a single numerical variable in bins, so its bars touch. If your x-axis values are categories, use a bar graph. If they’re numerical intervals, use a histogram.

How do you read a histogram?

Pick a bar, then check two things: which bin (interval) it represents on the x-axis, and how high it goes on the y-axis. Example: a bar over the bin 70-79 reaches a height of 12 – that means 12 data values fall between 70 and 79. To find the total count, add up the heights of all bars.

What’s a bin (or class), and how do I choose one?

A bin is a numerical interval that groups values together. For test scores 0-100, common bin widths are 5, 10, or 20 points. A good rule of thumb is to aim for somewhere between 5 and 15 bins total. Too few bins hides patterns; too many makes the chart look noisy. A data set with 50 values often looks good with 6 to 8 bins.

What’s frequency vs. Relative frequency?

Frequency is the raw count of values in a bin. Relative frequency is that count divided by the total number of data points – it expresses each bin as a fraction or percent of the whole. Example: if 12 of 50 students scored in 70-79, the frequency is 12 and the relative frequency is \(\frac{12}{50} = 0.24\), or 24%.

What does the shape of a histogram tell me?

The shape describes the overall distribution. Symmetric (roughly bell-shaped) means values cluster around the center. Right-skewed (long tail on the right) is common for incomes and reaction times. Left-skewed (long tail on the left) is common for exam scores when most students do well. Bimodal (two peaks) might mean two underlying groups, like male and female heights mixed together.

How do I find the median from a histogram?

A histogram doesn’t show individual values, but you can estimate the median by finding the bin where the cumulative count passes half the total. If 50 students took a test and the bins from low to high have counts 4, 8, 14, 18, 6 (total 50), the median lies in the third bin (the cumulative count reaches 26 by the end of that bin, which crosses 25 – half of 50).

What’s an outlier on a histogram?

An outlier on a histogram appears as a short, isolated bar far from the main body of the data, with empty bins between it and the rest. Example: most scores cluster between 60 and 95, but a single value lands in the 20-29 bin with no values between. That isolated bar suggests an outlier worth investigating.

Why do some histograms have unequal bin widths?

Sometimes uneven widths make sense – for example, age groups 0-17, 18-64, \(\color{blue}{65+ \text{ on }}\) a population chart. In that case, the bar height should represent density (count per unit width), not raw count, so areas stay comparable. For most intro-level work, stick with equal bin widths and read the bars as counts.

Where do histograms show up on tests?

Middle-school state tests from grade 6 up, the SAT, ACT, GED, GRE, ASVAB, AP Statistics, and college placement tests. Typical questions: read off a frequency, compute relative frequency, find a total, identify the shape of the distribution, or estimate the median or quartiles.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to find mean, median, mode, and range
• How to find mean absolute deviation
• How to find range, quartile, and IQR
• How to interpret histograms
• How to graph a box plot