MathematicsChapter 11: Basic Statistics
Frequency Polygon and Pie Chart
A histogram uses bars.
Definition
A histogram uses bars. A frequency polygon joins the midpoints of the class tops (or the midpoints at class marks) with straight lines, often closing to the axis with a class of frequency zero at each end. A pie chart shows parts of a whole as angles of a circle: angle = (frequency / total) x 360 deg.
Formula
angle = (frequency / total) x 360 deg.
Overview
When to use which picture:
Frequency Polygon
Plot class mark (mid-value) on the x-axis and frequency on the y-axis. Join with straight lines. Two polygons on one grid compare two data sets. Unequal class widths need care: the height must still represent frequency density if the histogram used density.
Examples Test scores two classes · Close to zero at both ends · Do not join bar corners of a histogram and call it a polygon
Pie Chart
Only for parts of one total. Find each angle, check they sum to 360 deg (small rounding is allowed). A pie is a poor choice for many tiny categories or for showing change over time (use a line graph).
Examples Favourite sports in one class · Angle 90 deg = a quarter · Not for temperature vs month
In simple words
A histogram can have unequal class widths; then bar area (not raw height) must show frequency. A pie chart cannot show unequal widths at all because it is not on a number line.
Key points
- polygon joins midpoints
- pie uses 360 deg
- class mark vs frequency
- compare two sets
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Frequency Polygon and Pie Chart
Sticky Notes · Quick Revision
Core Idea
- A histogram uses bars.
Key Points
- polygon joins midpoints
- pie uses 360 deg
Simple Check
- Explain frequency polygon and pie chart in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- A histogram can have unequal class widths; then bar area (not raw height) must show frequency. A pie chart cannot show unequal widths at all because it is not on a number line.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- polygon joins midpoints
- pie uses 360 deg
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