Mathematics
Grade 8
15 min
Interpret histograms
Interpret histograms
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1
Introduction & Learning Objectives
Learning Objectives
Define a histogram and identify its key components (intervals/bins, frequency, axes).
Extract specific frequency information from a given histogram.
Describe the overall shape of a data distribution shown in a histogram (e.g., symmetric, skewed, uniform).
Identify the range of data values and the most frequent interval from a histogram.
Compare and contrast data sets represented by different histograms.
Make inferences about a data set based on its histogram.
Ever wonder how stores know what sizes of clothes to stock the most? Or how meteorologists summarize daily temperatures? 🤔 Histograms help us see patterns in large amounts of data!
In this lesson, you'll learn what histograms are, how to read their different parts, and how to interpret the sto...
2
Key Concepts & Vocabulary
TermDefinitionExample
HistogramA type of bar graph that shows the frequency of data within specific intervals. Unlike bar graphs, the bars in a histogram touch each other to indicate continuous data.A histogram showing the number of students who scored within certain ranges on a math test (e.g., 60-69, 70-79, 80-89).
FrequencyThe number of times a particular data value or range of values occurs in a data set. In a histogram, it's represented by the height of each bar.If a bar on a histogram reaches a height of 10, it means 10 data points fall within that bar's interval.
Interval (Bin)A range of data values that each bar in a histogram represents. All intervals must be of equal width.In a histogram of student heights, an interval might be '150 cm - 159 cm', meaning all...
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Core Formulas
Rule for Reading Frequency
The height of each bar in a histogram directly corresponds to the frequency (or count) of data points that fall within that bar's interval.
To find out how many data points are in a specific range, locate the bar representing that range and read its height on the y-axis.
Rule for Understanding Intervals (Bins)
Each bar represents a continuous range of data values (an interval or bin), and all intervals must be of equal width.
The x-axis labels define these intervals. Data points are grouped into these ranges, not individual values. For example, '10-20' means all values greater than or equal to 10 and less than 20 (or less than or equal to 20, depending on the convention).
Rule for Describing Distribution Shape
Observe the overa...
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Challenging
A histogram of customer ages at a comic book store shows two distinct, separate peaks: one in the 12-16 age range and another in the 30-34 age range. This type of distribution is called bimodal. What is the most likely inference?
A.The store is most popular with 23-year-olds.
B.Most customers are either very young or very old.
C.The store has an equal number of customers in every age group.
D.The store appeals to two different primary age demographics, likely teenagers and adults.
Challenging
A histogram shows the number of goals scored per game by a soccer team over 25 games. The distribution is heavily skewed right, with a peak frequency of 12 in the '0-1 goals' interval. What does this imply about the team's performance?
A.The team is very consistent, scoring 2-3 goals in almost every game.
B.The team's average goals per game is likely higher than its median goals per game.
C.The team scores a high number of goals in most games.
D.The team's median goals per game is likely higher than its average goals per game.
Challenging
A histogram of 20 students' test scores is perfectly symmetric, centered around the 80-89 interval. Five new students join the class and they all score between 50-59. How will the addition of this new data most likely change the shape of the histogram?
A.It will become skewed to the left.
B.It will become skewed to the right.
C.It will remain symmetric but the center will shift down.
D.It will become a uniform distribution.
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