Mathematics
Grade 10
15 min
Create histograms
Create histograms
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1
Introduction & Learning Objectives
Learning Objectives
Define a histogram and distinguish it from a bar chart.
Organize raw numerical data into a frequency distribution table.
Determine an appropriate number of bins and calculate the bin width for a given dataset.
Construct an accurate histogram on a labeled coordinate plane, including a title and axis labels.
Interpret the shape (e.g., symmetric, skewed), center, and spread of a data distribution from a histogram.
Analyze real-world data by creating and interpreting histograms.
Ever wondered how to visually represent the test scores of your entire class to see the overall performance at a glance? 📊
This tutorial will guide you through the process of creating a histogram, a powerful tool for visualizing the distribution of numerical data. You'll learn...
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Key Concepts & Vocabulary
TermDefinitionExample
HistogramA graphical representation of the distribution of numerical data. Data is grouped into continuous, non-overlapping intervals (bins), and the frequency of data in each bin is represented by the height of a bar. The bars in a histogram touch each other.A graph showing the number of students who scored in the ranges 50-59, 60-69, 70-79, etc., on a math test.
Frequency Distribution TableA table that organizes data by listing the class intervals (bins) and the number of data points (frequency) that fall into each one.A table with two columns: 'Test Score Range' (e.g., 80-89) and 'Number of Students' (e.g., 12).
Bin (or Class Interval)A range used to group data in a histogram. All bins in a histogram are typically of equal width.In a histogram...
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Core Formulas
Bin Width Calculation
Width = (Maximum Value - Minimum Value) / (Number of Bins)
This formula is used to calculate the width of each bin. After calculating, it's common to round the result up to a more convenient number (e.g., round 4.3 up to 5) to make the bin intervals easier to read.
Sturges' Rule for Number of Bins
k = 1 + 3.322 * log_{10}(n)
A common guideline for determining a good starting number of bins (k) for a histogram, where 'n' is the total number of data points. The result is often rounded to the nearest integer. This is a suggestion, not a strict rule.
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Challenging
You are given the commute time data (n=30, range 15 to 55). You create two histograms: Histogram 1 with 3 bins and Histogram 2 with 15 bins. Which statement best describes the likely visual outcome?
A.Histogram 1 will show the data's skewness clearly, while Histogram 2 will look like a flat line.
B.Both histograms will look identical and show a perfect bell curve.
C.Histogram 1 may oversimplify the data, hiding key features, while Histogram 2 may be too 'noisy' and show too much random variation.
D.Histogram 2 will be easier to interpret because it has more bars.
Challenging
A histogram is created for a dataset of 50 points with a bin width of 5. The first bin is [10, 15) with a frequency of 8, and the second bin is [15, 20) with a frequency of 12. If the bin width is doubled to 10, what is the frequency of the new first bin, [10, 20)?
A.10, the average of the two original frequencies.
B.12, the higher of the two original frequencies.
C.20, the sum of the two original frequencies.
D.It is impossible to determine without the raw data.
Challenging
A histogram has 5 bins of equal width and represents 35 data points. The data ranges from a minimum of 20 to a maximum of 70. The frequencies for the bins are 4, 9, 12, 7, and 3. In which bin does the median of the dataset lie?
A.The second bin
B.The third bin
C.The fourth bin
D.The fifth bin
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