If a cutoff falls inside a histogram class, the bar tells you how many values are in the whole class. It cannot tell you exactly how many values are on either side of the cutoff. Use complete classes to find the minimum, then include the split class to find the maximum.
The 2027 SEC G3 Mathematics K310 syllabus includes interpreting histograms with equal class intervals. This guide uses an equal-width histogram with frequency on the vertical axis and shows why two similar-looking questions can need different answers.
- Read the endpoints of each interval.
- Add the frequencies for classes entirely on the required side.
- Check whether the cutoff splits another class.
- State the exact count or the possible range.
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Read the classes before adding
Imagine an equal-width histogram of waiting times. The first bar covers 0 to under 5 minutes and has frequency 6. The next bar covers 5 to under 10 minutes and has frequency 11. The last bar covers 10 to under 15 minutes and has frequency 8. The bars give a total of 25 observations.
Each time of exactly 10 minutes belongs to the last class because the second class ends just before 10. For a question asking how many waited at least 10 minutes, the answer is exactly 8.
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Worked example | How many waited at least 7 minutes?
All eight observations in the last class qualify. None of the first six qualify. The middle class contains 11 observations, but their exact values are unknown. If all 11 were below 7 minutes, only 8 people qualify. If all 11 were at least 7 minutes, 19 qualify.
So the possible count is from 8 to 19 inclusive. Multiplying 11 by the fraction of the class width above 7 would make an assumption about how waiting times are distributed within that class. The bar itself does not establish that assumption.
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CHAPTER 3 OF 4 · Back to contents
Change the wording and check the boundary
Ask how many waited less than 10 minutes. The answer is exactly 6 + 11 = 17. Now ask how many waited at most 10 minutes. Everyone in the first two classes qualifies, and anyone whose time is exactly 10 minutes also qualifies. The histogram does not show how many of the eight in the last class waited exactly 10 minutes.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Can the original list settle the question?
Yes. Count the individual waiting times that satisfy the condition. Grouping hides that detail.
What should a parent ask during practice?
Ask the student to point to the bar crossed by the cutoff and name the group that is definitely included before calculating the range.