Cumulative Frequency Calculator

A cumulative frequency table adds up as it goes. Each row shows the combined count of all observations up to and including that bin. By the final row, the cumulative count always equals n.

The ogive is the line chart version: it starts at zero and climbs to 100%, forming a characteristic S-shape for bell-shaped data or a J-curve for right-skewed data. The name comes from an architectural term for a pointed arch.

Reading the ogive is simple and useful. The 50% line gives you a visual estimate of the median. The 25% and 75% lines give the quartiles. Comparing two overlaid ogives is a quick visual test of whether two samples come from the same distribution.

Most courses focus on histograms and skip ogives, but ogives answer a different question. With a histogram you see “how many values are in each bin.” With an ogive you see “what fraction of my data is below this value” — read directly off the chart without arithmetic.

Worked example: data [5, 7, 8, 10, 12, 15, 15, 18, 20, 22], 4 bins. Bin width is (22 − 5) / 4 = 4.25.

• Bin 1: [5.00, 9.25) holds 5, 7, 8 -> freq 3, cumulative 3 (30%)
• Bin 2: [9.25, 13.50) holds 10, 12 -> freq 2, cumulative 5 (50%)
• Bin 3: [13.50, 17.75) holds 15, 15 -> freq 2, cumulative 7 (70%)
• Bin 4: [17.75, 22.00] holds 18, 20, 22 -> freq 3, cumulative 10 (100%)

Note the last bin is closed at both ends. Every other bin excludes its upper bound, but the largest value has to land somewhere, so it goes in the top bin rather than falling off the end.

The cumulative count reaches 50% exactly at 13.50, and the median of this data is (12 + 15) / 2 = 13.5. That is not luck. Reading the 50% line off an ogive is how you estimate a median from binned data when the raw numbers are gone.

Enter your comma-separated data and choose a bin count. The table and ogive update together. Use the same bin count you used for the frequency distribution if you want to compare the two charts directly.