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The Data Detective
The Data Detective
A market researcher needs to analyze the ages of customers visiting a shopping center. With hundreds of customers, plotting each individual age would create a messy scatter of points. Instead, they group ages into ranges (0-10, 10-20, 20-30, etc.) and create a histogram - a powerful visual tool that reveals the shape and distribution of their data at a glance.
What is a histogram?: A histogram is a statistical diagram used to display grouped continuous data.
Key features:
- Bars touch (no gaps)
- y-axis shows frequency density
- Area of each bar = frequency for that class
Mathematics glossary
- What is a histogram?
- A histogram is a statistical diagram used to display grouped continuous data. Key features: - Bars touch (no gaps) - y-axis shows frequency density - Area of each bar = frequency for that class
- What is the modal class in a histogram?
- The modal class is the class interval with the highest frequency density. It is the class represented by the tallest bar on the histogram. Note: If class widths are equal, the modal class also has the highest frequency.
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Drawing Histograms: Step-by-Step
- Organize Data: Create a frequency table with class intervals
- Calculate Class Widths: Find the width of each interval
- Calculate Frequency Density: Frequency ÷ Class Width for each interval
- Choose Scales: X-axis for class boundaries, Y-axis for frequency density
- Draw Bars: No gaps, height = frequency density, width = class width
- Label Everything: Axes, title, and include units
Common Exam Tips:
- Always use frequency density, not frequency, on the y-axis
- Check class boundaries carefully (inclusive/exclusive)
- No gaps between bars (unlike bar charts)
- Area of each bar equals the frequency
- Use class midpoints for mean estimation
Now try it yourself
Quiz · Question 1 of 14
A histogram shows the heights (cm) of plants in a garden with the following frequency densities: - 0 =< h < 5: frequency density = 4 - 5 =< h < 15: frequency density = 3 - 15 =< h < 25: frequency density = 6 - 25 =< h < 40: frequency density = 2 What is the modal class?
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This topic in real past papers
Every real exam question we've found on histograms, with a full worked answer.