Frequency Polygons

Step 1: Calculate Midpoints

• For each class interval, find the midpoint using the formula: $Midpoint = \frac{Lower \, Bound + Upper \, Bound}{2}$
• Ensure that the midpoints are calculated consistently for all groups in the frequency table.

Step 2: Plotting Points

• Use the horizontal axis ($x$) for the midpoints and the vertical axis ($y$) for the frequencies.
• Mark each coordinate $(midpoint, frequency)$ clearly on the grid.

Step 3: Connecting the Data

• Join the plotted points in sequence from left to right using straight lines and a ruler.
• Do not connect the first point to the last point, and do not draw lines down to the x-axis unless the frequency for a specific boundary class is zero.

• Check the Midpoints: Examiners often provide intervals like $10 \le x < 20$. Always verify your midpoint calculation ($15$ in this case) before plotting to avoid systematic errors.

• The 'Floating' Rule: A common mistake is closing the polygon by drawing lines to the origin or the end of the x-axis. Unless the table includes a frequency of $0$ for those points, leave the line 'floating'.

• Labeling Axes: Ensure the x-axis is labeled with the actual variable being measured (e.g., 'Mass in kg') rather than just the word 'Midpoint'.

• Interpreting Peaks: The highest point on the polygon represents the modal class. If you are asked for an estimate of the mode, provide the midpoint of that highest peak.

• Plotting at Boundaries: Students often mistakenly plot the frequency at the upper or lower bound of the class interval. This shifts the entire distribution and results in an inaccurate representation.

• Curved Lines: Frequency polygons must be drawn with straight lines. Using a curve creates a frequency curve, which is a different statistical tool used for modeling continuous distributions.

• Inconsistent Scales: Ensure the frequency axis starts at zero and uses equal increments. An inconsistent scale can visually distort the 'spread' of the data.