Key takeaway: A histogram is a bar graph for numerical data in which each bar covers an equal-width interval and its height shows how many values fall in that interval.
Grade 66.SP.B.4Statistics and Data
Definition of Histogram
A histogram groups numerical data into equal-width intervals, called bins, and draws one bar per bin. The height of a bar is the number of data values inside that interval.
The bars touch because the intervals run continuously along a number line, one after another. That is the main visual difference from a bar graph of categories, whose bars are separated. A histogram does not show individual values, only how many fall in each range, so it suits large data sets. Its overall shape tells where data cluster, whether it is symmetric or skewed, and how spread out it is.
Formula and notation
Bins are written as ranges that do not overlap, such as 0 to 9, 10 to 19 and so on. The total number of values is the sum of the bar heights:
\[n = f_1 + f_2 + f_3 + \text{…}\]
where \(f_1, f_2, \text{…}\) are the frequencies. Both axes carry labels: the horizontal one names the variable and the vertical one says “frequency”.
Key facts
- Every bin must have the same width, and no bins may overlap.
- Adding all bar heights gives the total number of data values.
- Individual data values cannot be read from the graph, only counts per interval.
- The tallest bar marks the interval that holds the most values.
Histogram example
A survey of 33 students gave these commute-time bins (minutes): 0-9 has 4, 10-19 has 9, 20-29 has 12, 30-39 has 6, 40-49 has 2. How many students commute less than 20 minutes, and what fraction of the class is that?
-
Add the first two bars: \(4 + 9 = 13\) students.
-
Check the total: \(4 + 9 + 12 + 6 + 2 = 33\).
-
Fraction: \(\frac{13}{33} \approx 0.39\).
13 students commute less than 20 minutes, which is about 39% of the class.
Common mistake
Watch out
Cleo reads the tallest bar, 20-29, and says “the students commute 12 minutes.”
Why it is wrong
The height 12 is a count of students, not a time. The tallest bar tells that 12 students have commutes between 20 and 29 minutes. The time scale is on the horizontal axis.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Statistics and Data