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Frequency Polygon and Pie Chart
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.
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Frequency Polygon and Pie Chart
What is it?
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.
In simple words
Frequency Polygon and Pie Chart is a core idea in this chapter. Learn the meaning first, then the main parts, then one clear example.
Examples
- Test scores two classes
- Close to zero at both ends
- Do not join bar corners of a histogram and call it a polygon
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.
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).
Recommended for Class 9
Full school-level explanation
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.
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.
Remember
- class mark vs frequency
- compare two sets
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).
Remember
- parts of one total
- angles sum 360
Examples
- Favourite sports in one class
- Angle 90 deg = a quarter
- Not for temperature vs month
Remember
- polygon joins midpoints
- pie uses 360 deg
- histogram area
- pie is parts of a whole
- class mark vs frequency
- compare two sets
- parts of one total
- angles sum 360
Deeper understanding
Go beyond memorising Frequency Polygon and Pie Chart. Connect the definition to reasons, relationships, exceptions, and exam wording.
Exam focus
Quick revision
- polygon joins midpoints
- pie uses 360 deg
- histogram area
- pie is parts of a whole
- FREQUENCY POLYGON: Plot class mark (mid-value) on the x-axis and frequency on the y-axis. Join with straight lines. Two
- PIE CHART: Only for parts of one total. Find each angle, check they sum to 360 deg (small rounding is allowed).
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.
For long answers on Frequency Polygon and Pie Chart: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- polygon joins midpoints
- pie uses 360 deg
- histogram area
- pie is parts of a whole
Important formulas
- polygon joins midpoints
- pie uses 360 deg
- histogram area
Common exam traps
- 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 o
- 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 o
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- 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 o
- 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 o
- 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 o
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
polygon joins midpoints
pie uses 360 deg
histogram area
pie is parts of a whole
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 axi
- 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 axi
- Example
- Test scores two classes
- Critical warning
- A histogram can have unequal class widths; then bar area (not raw height) must show frequency. A pie chart cannot show u
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Exam Practice
Define
Q1. Define Frequency Polygon and Pie Chart.
Explain
Q2. Explain: FREQUENCY POLYGON.
Example
Q3. Give one clear example of Frequency Polygon and Pie Chart and say why it fits.
Mistake
Q4. State one common mistake students make about Frequency Polygon and Pie Chart.
Exam note
Q5. Write a short exam note on Frequency Polygon and Pie Chart: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.