Histogram
In short: Histogram draws touching bars over equal-width ranges of a number scale, with each bar as tall as the count of values that land in its range.
6th GradeStatistics6.SP.B.4
What is Histogram?
A histogram sorts a large set of numbers into equal-width bins and draws one bar per bin. Instead of showing every value, it shows how the data pile up: where most values sit and where few do.
Along the bottom, the scale is cut into ranges like 0 to 9 minutes, then 10 to 19, then 20 to 29, with no gaps between neighbors. Bar heights are counts, so all heights together equal the number of data values.
How to spot it
- A graph has touching bars over a numerical scale such as minutes, ages or heights.
- The data set is large, with dozens or hundreds of values, so single dots would be too many.
- A question asks how many values fall within a range, or which interval has the most.
- You are asked to describe the shape: symmetric, skewed or with a peak.
The method
- Choose equal-width intervals that cover every value, and label the horizontal axis.
- Count how many data values fall in each interval, using each boundary rule consistently.
- Draw touching bars whose heights equal those counts.
- Add the heights to check the total, then describe the peak, spread and shape.
Histogram: solved example
Problem
The histogram above summarizes the commute times of 40 workers in a Denver office. How many commute for less than 30 minutes, and what fraction of the workers is that?
Solution
Add the first three bars: \(4 + 11 + 15 = 30\) workers.
The fraction is \(\frac{30}{40} = \frac{3}{4}\). So 30 workers, which is three fourths, commute less than 30 minutes.
Try it
Question 1
Which interval holds the most workers in the histogram above, and how many?
Show the answer
The 20-29 interval, with 15 workers.
Question 2
Why do the bars of a histogram touch, while the bars of a bar graph for categories do not?
Show the answer
The intervals form a continuous scale with no gaps between them, whereas categories are separate groups.
Histogram vs. Dot Plot
A histogram groups numbers into intervals and loses the exact values, but it handles big data sets cleanly. A dot plot shows each value as its own dot, which is exact but gets crowded quickly. Choose by the size of the data.
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Related words
Whole dictionary: A–Z · 6th Grade · Statistics