📊 Charting Success: Histograms & Frequency Polygons Made Easy!

Data comes alive when we **visualise** it. For O Level Mathematics, being able to draw and interpret histograms and frequency polygons can earn quick marks. Remember, a histogram’s bars touch because the data is continuous, and the **area** of each bar is proportional to its frequency. When class widths vary, use **frequency density** so that

\text{frequency density}=\dfrac{\text{frequency}}{\text{class width}}

. Connecting the mid-points of the tops of the bars gives a frequency polygon that makes trends even clearer.

Label the $x$ -axis with class boundaries and the $y$ -axis with frequency density.
Calculate class mid-points before sketching a frequency polygon.
Use identical scales when you compare two data sets on one diagram.
Check titles, units, and a neat key to secure presentation marks.

Worked Example: From Table to Diagram

Problem: The masses (kg) of 50 mangoes are grouped as follows: 60–64 (5), 65–69 (12), 70–74 (18), 75–84 (10), 85–99 (5). Draw a histogram and overlay a frequency polygon.

Step 1: Work out each class width: 5, 5, 5, 9, 14.
Step 2: Calculate frequency density, e.g. for 75–84:
$\frac{10}{9}\approx1.11$
. Repeat for every class.
Step 3: On graph paper plot bars whose heights equal their frequency densities and whose widths match the class intervals.
Step 4: Find each class mid-point (e.g. $67$ for 65–69) and join these points with straight lines to form a frequency polygon.
Step 5: Review axes labels, scales and a clear legend. Great work! Keep practising with past-paper data sets to perfect the technique.