How this instrument works
A frequency polygon shows the shape of a grouped data set as a line graph: instead of drawing a bar for each class the way a histogram does, it plots a single point at each class's midpoint — the value exactly halfway between the class's lower and upper edges — at a height equal to that class's count, then connects the points with straight line segments. The resulting shape traces the same distribution a histogram's bars would show, just as an outline rather than filled rectangles.
The binning itself is identical to this site's frequency-distribution and histogram instruments: the data's range is split into equal-width classes, width = (maximum − minimum) / number of classes, and every value is counted into exactly one class. Frequency-polygon's distinctive step is converting each class's edges into a single representative midpoint — lower edge plus half the class width — before pairing it with that class's count, which is the specific input a frequency-polygon chart needs.
Frequency polygons are especially useful for comparing two or more distributions on the same chart, since overlapping outlines are far easier to read at a glance than overlapping sets of bars. A line-based shape also makes it easier to see whether a distribution is roughly symmetric, skewed toward one side, or has more than one peak — patterns that can be harder to judge from bars alone.
- Enter your raw numbers into Data set (midpoints) — any order, separated by commas, spaces or new lines.
- Set Number of classes to how many groups you want the range split into.
- Read Class width to confirm how wide each interval turned out to be.
- Read Midpoint frequency table (midpoint: count) for the exact points to plot — each class's midpoint paired with its count, ready to connect with straight lines.
- Want the same data as an interval table or as bars instead? This site's frequency-distribution and histogram instruments use this identical binning.
Worked example — ten measurements, 5 classes
Ten measurements are recorded as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Enter those values into Data set (midpoints) and set Number of classes to 5. Class width comes out to (10−1)/5 = 1.8, giving five class edges at 1.00, 2.80, 4.60, 6.40, 8.20, and 10.00 — and five midpoints at 1.9, 3.7, 5.5, 7.3, and 9.1 (each edge plus half of 1.8).
Midpoint frequency table (midpoint: count) reads '1.90: 2 | 3.70: 2 | 5.50: 2 | 7.30: 2 | 9.10: 2' — every class catches exactly two of the ten values, so a frequency polygon plotted from these five points would trace a perfectly flat line at height 2 across the middle of the range, dropping to zero just past 1.9 and just past 9.1 where the standard convention anchors the line back down to the axis on either side.
Questions
How is a frequency polygon different from a histogram on this site?
They're built from the exact same binning — same class width, same counts per class — but represent the result differently. A histogram frames each class's count as a bar's height, anchored at its edges. A frequency polygon instead plots a single point at each class's midpoint, at that same height, and connects the points with straight lines, producing an outline rather than filled bars. Use the polygon form when you want to compare two or more distributions on one chart, since overlapping outlines read more clearly than overlapping bars.
Why plot at the midpoint instead of at the class edges?
A class's count applies to the whole interval, not to any single point within it, so the midpoint is the natural single value to represent the entire class when only one point can be plotted. Using the midpoint rather than, say, the lower edge, keeps the plotted point centered over the range of values it actually represents.
Do I need to plot the endpoints touching the axis myself?
The standard frequency-polygon convention anchors the line down to zero at one class-width before the first midpoint and one class-width after the last, so the shape closes into a readable outline rather than floating above the axis. This calculator gives you the midpoint/count pairs for the classes themselves; adding those two zero-height anchor points when you draw the chart is a manual finishing step.
Can I compare two data sets using frequency polygons?
Yes — that's one of the main reasons to choose a frequency polygon over a histogram in the first place. Plot two data sets' midpoint/count pairs on the same axes as two separate lines (using the same number of classes and, ideally, the same class boundaries for both), and the two outlines can be compared directly for shape, peak location, and spread in a way that two sets of overlapping bars usually can't.
Does changing the number of classes change the shape of the polygon?
Yes, sometimes substantially — fewer, wider classes smooth out small fluctuations in the data but can hide real structure like a second peak, while more, narrower classes reveal finer detail but can make the line look noisy or jagged, especially with a smaller data set. There's no single right number of classes; it's worth trying a couple of values and picking whichever best reveals the pattern you're investigating.