Mathematics
Grade 10
15 min
Interpret histograms
Interpret histograms
What you'll learn
- Identify the title, labels, and scale of a given histogram and explain what each represents.
- Answer at least 3 out of 4 questions about data presented in a histogram, such as 'How many students are between 10 and 12 years old?'
- Compare two different intervals on a histogram and explain which interval contains more data points with supporting evidence from the graph.
- Create a simple question that can be answered using the data presented in a given histogram.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Describe the shape of a data distribution (skewness, modality, symmetry) by analyzing its histogram.
Estimate the center (median) and spread (range) of a dataset from its histogram.
Identify potential outliers, gaps, and clusters within a histogram.
Calculate the relative frequency of a data interval using the information presented in a histogram.
Compare and contrast two different data distributions by interpreting their respective histograms.
Explain how the area of the rectangular bars in a histogram relates to the proportion of data in each interval.
How can a simple set of rectangles reveal the story behind a thousand test scores or the performance of your favorite athlete? 📊
A histogram is a powerful two-dimensional figure that uses rectangular ba...
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Key Concepts & Vocabulary
TermDefinitionExample
HistogramA graphical display of data using adjacent rectangular bars. The horizontal axis represents continuous data divided into intervals (bins), and the vertical axis represents the frequency (or relative frequency) of data points in each bin.A histogram showing the heights of Grade 10 students might have bins like 150-155 cm, 155-160 cm, etc., on the x-axis, and the number of students in each height range on the y-axis.
Bin (or Class Interval)The range of values that a single bar in a histogram represents. All bins in a histogram are typically of equal width.In a histogram of exam scores, a bin could be '70-79', representing all scores from 70 up to (but not including) 80.
FrequencyThe number of data points that fall within a specific bin. It is represe...
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Core Formulas
Area Proportionality Principle
Area_{bar} \propto \text{Frequency}
The area of each rectangular bar is proportional to the number of data points in its bin. Since bin widths are usually equal, the height of the bar is also proportional to the frequency. This geometric property is key to visual interpretation.
Relative Frequency Calculation
f_{rel} = \frac{\text{Frequency of bin}}{\text{Total Frequency}} = \frac{f_i}{\sum f}
To find the proportion or percentage of data that falls within a specific interval, divide the frequency of that bin by the total number of data points (the sum of all frequencies).
Median Estimation
\text{Median Position} = \frac{n+1}{2}
To estimate the median from a histogram, first find the total number of data points (n). Calculate the positio...
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Challenging
An analyst creates a histogram of daily stock price changes with a bin width of $1. The histogram appears unimodal and symmetric. If the analyst re-creates the histogram with a much smaller bin width of $0.10, what new feature is most likely to be revealed?
A.hidden bimodal shape or gaps might become visible.
B.The total frequency of the data will change.
C.The range of the data will increase.
D.The distribution will definitely become skewed right.
Challenging
A histogram of the salaries for all employees at a large company shows a strong right skew. What is the most likely real-world reason for this shape?
A.All employees earn roughly the same salary, clustered around the average.
B.There are two distinct pay scales, such as for administrative staff and factory workers.
C.Most employees earn a moderate salary, but a few executives earn very high salaries, creating a long tail to the right.
D.The company primarily hires recent graduates, and very few senior employees remain.
Challenging
[Image of two histograms. Histogram A shows test scores for a class of 20 students. Histogram B shows scores for a class of 100 students. Both histograms are unimodal and skewed left, with identical shapes and bin intervals. The modal class in both is '80-90'.] What can be concluded by comparing the two histograms?
A.The number of students who scored in the '80-90' range is the same for both classes.
B.The proportion (or percentage) of students who scored in the '80-90' range is likely similar for both classes.
C.Class A performed better overall than Class B because its bars are shorter.
D.Class B has a larger range of scores than Class A.
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Frequently asked questions
What grade level is "Interpret histograms"?
Interpret histograms is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Interpret histograms?
You'll be able to: Identify the title, labels, and scale of a given histogram and explain what each represents; Answer at least 3 out of 4 questions about data presented in a histogram, such as 'How many students are between 10 and 12 years old?'….
Is "Interpret histograms" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Interpret histograms?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.