How do you draw a frequency polygon for grouped data?

Get Organized: The Frequency Distribution Table: First, you need to wrangle your data into a table. List your class intervals and how often each one appears (the frequencies).

Find the Sweet Spot: Calculate the Midpoints: Remember that midpoint thing? Time to put it into action. Add the upper and lower limits of each class, divide by two, and boom – you’ve got your midpoint. For instance, if your class interval is 20-30, the midpoint is (20+30)/2 = 25. Easy peasy.

Draw the Axes: Now, draw a line horizontally (the x-axis) and another one vertically (the y-axis). The x-axis is where your midpoints will live, and the y-axis is for your frequencies. Make sure your scales are wide enough to fit all your data!

Plot the Points: This is where the magic happens. For each class, find its midpoint on the x-axis and then go up to the corresponding frequency on the y-axis. Put a dot there.

Connect the Dots: Grab a ruler (or don’t, if you’re feeling rebellious) and connect those dots with straight lines. You should start to see a shape emerging!

Close the Deal: Completing the Polygon: Here’s the slightly weird part. To make it a polygon (a closed shape), you need to bring the lines down to the x-axis on both ends. Basically, you’re adding “imaginary” classes with zero frequency. To do this, figure out the class width (how wide each interval is). Then, subtract that width from your smallest midpoint to get the x-coordinate for your first zero-frequency point. Add the width to your largest midpoint to get the x-coordinate for the last one. Plot those points, and connect ’em up!