Mathematics
Grade 8
15 min
Create histograms
Create histograms
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a histogram and explain its purpose in data analysis.
Distinguish between a bar graph and a histogram.
Organize raw numerical data into a frequency table with appropriate intervals (bins).
Determine suitable bin widths for a given dataset.
Correctly label the axes of a histogram.
Construct a histogram from a frequency table.
Interpret basic features of a histogram, such as its shape and spread.
Ever wonder how to quickly see patterns in a large set of numbers, like test scores or heights? 📊 Let's learn how to make a special kind of graph that helps us do just that!
In this lesson, you'll discover what histograms are and how to create them step-by-step. Understanding histograms is crucial for visualizing the distribution of numerical d...
2
Key Concepts & Vocabulary
TermDefinitionExample
HistogramA type of bar-like graph that displays the frequency distribution of numerical data. Unlike bar graphs, the bars in a histogram touch each other (unless an interval has zero frequency) because they represent continuous data ranges.A histogram showing the number of students who scored between 70-79, 80-89, and 90-100 on a math test.
Numerical DataData that represents quantities and can be measured or counted. This type of data can be ordered and used in calculations.Heights of students (e.g., 155 cm, 162 cm), ages of people (e.g., 13 years, 14 years), or test scores (e.g., 85, 92).
FrequencyThe number of times a particular value or, more commonly in histograms, a range of values (an interval or bin) appears in a dataset.If 5 students scored between 80 and 89...
3
Core Formulas
Consistent Bin Width
All bins (intervals) on the horizontal axis of a histogram must have the same width.
To accurately represent the distribution of data, each interval must cover the same range of values. Inconsistent bin widths can distort the visual representation of the data.
No Gaps Between Bars
The bars in a histogram must touch each other, unless an interval has zero frequency.
Histograms represent continuous numerical data, meaning there are no gaps between the data ranges. This distinguishes them from bar graphs, which typically show discrete categories with gaps between bars.
Proper Axis Labeling
The horizontal (x) axis represents the data intervals, and the vertical (y) axis represents the frequency (count) of data points within each interval.
Clear and a...
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Challenging
Consider the 'Student Test Scores' data. If the teacher changes the bin width to 5 (e.g., 60-64, 65-69, 70-74, etc.), what would be the frequency of the new 75-79 bin?
A.2
B.3
C.4
D.5
Challenging
A histogram has three bars for bins A, B, and C. The total number of data points is 40. The bar for bin B is twice as tall as the bar for bin A. The bar for bin C is four times as tall as the bar for bin A. What is the frequency of bin B?
A.10
B.20
C.30
D.15
Challenging
A student submits a histogram of class heights. The title is 'Favorite Sports', the x-axis has inconsistent bin widths (e.g., 150-155, 155-165), and the y-axis is not labeled. Which of these is the most critical error for understanding the data's distribution?
A.The missing y-axis label, because we don't know if it's frequency or percentage.
B.The incorrect title, because it completely misrepresents the data's subject.
C.The lack of color on the bars, because it makes the graph uninteresting.
D.The inconsistent bin widths, because it fundamentally distorts the shape and spread of the data.
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