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:
- 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
Watch this practice video for additional examples and reinforcement:
Related Topics
- How to Interpret Pie Graphs
- How to Solve Probability Problems
- How to Solve Permutations and Combinations
- How to Find Mean, Median, Mode, and Range of the Given Data
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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Histograms – Example 1:
Use the following Graph to complete the table.
Solution: The graph you see above is a histogram. This chart gives you a brief overview of the distance traveled over different days. The horizontal axis represents the days traveled and the vertical axis represents the distance. The points marked on the graph indicate the distance traveled in each day, according to which you can complete the relevant table. Check the distance during each day from the graph and write it in the table below. For example, the distance for day \(1\) is \(378\) and for day \(2\) is \(480\).
| Day | Distance (km) |
| 1 | 378 |
| 2 | 480 |
| 3 | 285 |
| 4 | 436 |
| 5 | 370 |
Histograms – Example 2:
Use the following Graph to complete the table.
Solution: Check the distance during each day from the graph and write it in the table below.
| Day | Distance (km) |
| 1 | 359 |
| 2 | 460 |
| 3 | 278 |
| 4 | 547 |
| 5 | 360 |
Exercises for Solving Histograms
The following table shows the number of births in the US from \(2007\) to \(2012\) (in millions).
Answer these questions based on the data of the graph.
1- During what period the percent of change was zero?
2- During what period there was the biggest decrease in the number of births?
3- What was the percent of change from \(2008\) to \(2012\)?
Download Histograms Worksheet
1- \(\color{blue}{2011- 2012}\)
2- \(\color{blue}{2009 – 2010}\)
3- \(\color{blue}{7\% }\)
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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 \(12/50 = 0.24\), 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, 65+ 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.
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