Mathematics
Grade 9
15 min
Create histograms
Create histograms
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1
Introduction & Learning Objectives
Learning Objectives
Define key terminology associated with histograms, including bin, frequency, and range.
Calculate the appropriate number of bins and the bin width for a given data set.
Organize raw numerical data into a frequency table.
Construct a complete and accurately labeled histogram from a frequency table.
Distinguish between a histogram and a bar graph based on the type of data and visual representation.
Make basic interpretations about the distribution of data from a histogram.
How many hours did your classmates spend on homework last night? 📚 A histogram can turn a long list of numbers into a clear picture that tells a story!
This tutorial will guide you through the process of creating histograms, a powerful tool for visualizing numerical data. You will learn...
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Key Concepts & Vocabulary
TermDefinitionExample
HistogramA type of bar graph used to represent the frequency distribution of continuous numerical data. The bars are adjacent to each other (they touch) to show that the data is continuous.A graph showing the number of students whose heights fall within specific ranges (e.g., 150-155 cm, 155-160 cm, 160-165 cm).
FrequencyThe number of times a data value or a value within a specific interval occurs in a data set.In the data set {2, 3, 3, 4, 5, 5, 5}, the frequency of the number 5 is 3.
Bin (or Class Interval)A range or interval used to group data in a histogram. All bins in a single histogram must have the same width.If analyzing exam scores, a bin could be 70-79, representing all scores from 70 up to (but not including) 80.
Bin WidthThe size of each bin or class inte...
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Core Formulas
Range Calculation
Range = Maximum Value - Minimum Value
Use this first to understand the spread of your data. This value is crucial for determining the bin width.
Guideline for Number of Bins (k)
k \approx \sqrt{n}
A common starting point for deciding how many bins to use, where 'n' is the total number of data points. The result is an approximation; you can adjust it to a convenient whole number.
Bin Width Calculation
Bin Width \approx \frac{\text{Range}}{\text{Number of Bins}}
After finding the range and deciding on the number of bins, use this formula to calculate the width of each bin. It's often best to round this result up to a simple, convenient number (like 5, 10, or 20).
4 more steps in this tutorial
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Challenging
A teacher has the test score data for 20 students from the tutorial (Range = 36). They consider two designs: Design 1 uses 4 bins (width of 10). Design 2 uses 9 bins (width of 4). Based on the tutorial's guideline (k ≈ √n) and the goal of clearly showing the data's distribution, which design is more appropriate and why?
A.Design 2 is better because more bins always provide more detail.
B.Design 1 is better because its number of bins (4) is closer to the guideline suggestion (√20 ≈ 4.5) and avoids making the graph too sparse.
C.Both designs are equally valid as long as the bin widths are consistent.
D.Design 2 is better because a smaller bin width is always more accurate.
Challenging
You have a data set of 35 student heights with a range of 23 inches. You calculate the recommended number of bins as k ≈ √35 ≈ 6. You then calculate the bin width as 23 / 6 ≈ 3.83 inches. To create practical, non-overlapping bins that cover the entire range, what is the most effective bin width to choose?
A.3.83 inches, to be precise.
B.3 inches, because you should always round down.
C.4 inches, because rounding up ensures the entire range is covered.
D.5 inches, to make the numbers easy to work with.
Challenging
A histogram is presented with five bins: 50-59, 60-69, 70-79, 80-89, and 90-99. No other information about the original data is given. What is the MOST accurate conclusion you can make about the range of the original data set?
A.The range is exactly 49 (99-50).
B.The range is exactly 40 (the difference between the midpoints).
C.The range could be as small as 31 (e.g., max of 90, min of 59).
D.The range must be less than 50, but cannot be determined exactly.
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