Ogive Maker
Paste your values or type a class table and get an ogive — the cumulative frequency graph — with the quartiles read off the curve by dashed guide lines and worked out in a table. Group raw data by Sturges', Scott's or Freedman–Diaconis rule or your own width, switch the axis to percent, and download the graph as SVG or PNG. Free, no sign-up, and your data stays in your browser.
Paste a column from a spreadsheet or type the values. If your numbers use decimal commas, separate them with semicolons.
n = 40 · 6 classes
Read off the curve
Show the graph as a table
| Class | Frequency | Cumulative frequency | Cumulative % |
|---|---|---|---|
| 40 – 50 | 5 | 5 | 12.5 |
| 50 – 60 | 8 | 13 | 32.5 |
| 60 – 70 | 13 | 26 | 65 |
| 70 – 80 | 9 | 35 | 87.5 |
| 80 – 90 | 4 | 39 | 97.5 |
| 90 – 100 | 1 | 40 | 100 |
Values read off the curve
56.25
Q1
65.38
Median
74.44
Q3
18.19
Interquartile range
| Measure | Height (p × n) | Class | L + ((p × n − F) ÷ f) × w | From the curve | From the raw data |
|---|---|---|---|---|---|
| Q1 | 10 | 50 – 60 | 50 + ((10 − 5) ÷ 8) × 10 | 56.25 | 56.75 |
| Median | 20 | 60 – 70 | 60 + ((20 − 13) ÷ 13) × 10 | 65.38 | 64.5 |
| Q3 | 30 | 70 – 80 | 70 + ((30 − 26) ÷ 9) × 10 | 74.44 | 72.25 |
The curve joins (upper boundary, running total) points with straight lines, so each value read off it assumes the values are spread evenly within their class — the grouped-data formula. The raw-data column uses the inclusive quartile method (Excel QUARTILE.INC), which can differ a little from a grouped estimate.
Title and figure style
Takes the title out of the image and sets the figure number in bold and the title in italics above it — the APA 7 layout.
How to Use the Ogive Maker
- 1. Choose your data. Pick Raw values to paste numbers, or A class table to type classes such as
40-50: 8, one per line, lowest first. - 2. Group raw data. For raw values, choose how the classes are made: Sturges' rule, Scott's rule, the Freedman–Diaconis rule, or a class width you set. Rounding the width to a convenient number gives classes like 40–50 rather than 41.7–52.3.
- 3. Read the curve. The dashed guides mark Q1, the median and Q3 on the curve. Add a percentile of your own, such as 90, to read that off too. Switch the vertical axis to cumulative percent if you want to read shares instead of counts.
- 4. Check the working. The table under the graph shows, for each reading, the height, the class it falls in and the grouped-data formula with your numbers.
- 5. Download. Take the SVG or PNG. With APA style figure on, the figure number and title go above the image and an optional note goes below.
How an Ogive Is Drawn
An ogive (say OH-jive) plots the running total of a frequency table against the upper boundary of each class, because the total is only complete once the whole class has been counted. The first point is zero at the lower boundary of the first class, and the points are joined by straight lines. This tool draws the usual less than ogive: the height at any value on the x axis is how many observations are below it.
A class table and its running totals
Class Frequency Cumulative 30-40 3 3 40-50 6 9 50-60 9 18 60-70 12 30 70-80 7 37 80-90 3 40
The points are (30, 0), (40, 3), (50, 9), (60, 18), (70, 30), (80, 37) and (90, 40). With n = 40, the median is read at height 20. That height is reached in the 60–70 class, so the median is 60 + ((20 − 18) ÷ 12) × 10 ≈ 61.67.
Reading Quartiles From the Curve
To find Q1, the median and Q3, read across from n ÷ 4, n ÷ 2 and 3n ÷ 4 on the vertical axis to the curve, then down to the horizontal axis. Reading across a straight segment is linear interpolation, and it gives the same answer as the grouped-data formula, Q = L + ((p × n − F) ÷ f) × w, where L is the lower boundary of the class containing the height p × n, F is the total below it, f is its frequency and w its width. The table spells that out for each reading.
A reading from the curve assumes the values are spread evenly within each class, so it is an estimate. For raw data, the tool also shows the exact quartile by the inclusive method (Excel's QUARTILE.INC); the two differ by a fraction of a class width. Courses and software define quartiles differently, so if your course uses another method, quote that one for the final answer and use the curve for the graph.
Class Limits and Class Boundaries
Classes written 40–49 and 50–59 are class limits: the gap between them exists only because of rounding. The boundaries are halfway between, at 39.5, 49.5 and 59.5, and those are what an ogive uses. When you type classes with gaps like these, the tool moves the boundaries to the midpoints for you and says so; the table shows the boundaries it used. Classes that touch (40–50, 50–60) are used as written. When the tool groups raw data itself, a value exactly on a boundary counts in the class above it.
- Label both axes. The x axis is the variable with its unit; the y axis is Cumulative frequency or Cumulative percent.
- Use equal class widths. The straight-line assumption is easiest to defend when classes have one width.
- Say how the classes were made. In a paper, give the width or the rule in the figure note.
Frequently Asked Questions
- What is an ogive in statistics?
- An ogive is a graph of cumulative frequency. It plots the running total of a frequency table against the upper class boundaries and joins the points with straight lines. You can read from it how many observations lie below any value, and estimate the median, quartiles and percentiles.
- How do you find the median from an ogive?
- Find n ÷ 2 on the vertical axis, draw a horizontal line across to the curve, then a vertical line down to the horizontal axis. The value where it lands is the median. This tool draws those guides for you and works the same value out with the grouped-data formula.
- How do you find the quartiles from an ogive?
- Read the curve at n ÷ 4 for the lower quartile Q1 and at 3n ÷ 4 for the upper quartile Q3. The interquartile range is Q3 − Q1. Quartiles read from a graph of grouped data are estimates, and they can differ slightly from quartiles calculated on the raw values.
- Why is the ogive plotted at the upper class boundary?
- Because the running total only includes a whole class once its upper boundary is reached. At the lower boundary of the first class nothing has been counted, so the curve starts at zero there and reaches n at the upper boundary of the last class.
- What is the difference between an ogive and a histogram?
- A histogram shows how many values fall in each class. An ogive shows how many fall below each class boundary, so it always rises and ends at the total. Use a histogram to see the shape of the data and an ogive to read medians, quartiles and percentiles.
- Can I make an ogive from raw data instead of a table?
- Yes. Paste the values, choose how to group them, and the tool builds the frequency table and the ogive from it. Each class includes its lower boundary and excludes its upper one, except the last class, which includes both so the maximum is counted.