Ogive Maker | Free Cumulative Frequency Graph

Class	Freq.	Relative	Cum.	Cum. %
[40, 50)	4	3.3%	4	3.3%
[50, 60)	19	15.8%	23	19.2%
[60, 70)	32	26.7%	55	45.8%
[70, 80)	34	28.3%	89	74.2%
[80, 90)	22	18.3%	111	92.5%
[90, 100]	9	7.5%	120	100%
Total	120	100%

Class

Freq.

Relative

Cum.

Cum. %

[40, 50)

3.3%

[50, 60)

15.8%

19.2%

[60, 70)

26.7%

45.8%

[70, 80)

28.3%

74.2%

[80, 90)

18.3%

111

92.5%

[90, 100]

7.5%

120

100%

Total

120

100%

How to make an ogive

Paste your raw data, or choose “Frequency table” on the Data tab and enter classes with frequencies.
Pick clean classes in the Bins tab (for example width 10 starting at 0).
Choose Frequency, Relative or Percent for the y-axis. Percent makes percentiles easy to read.
Switch on “Show bars” in the Design tab to draw the cumulative histogram under the curve.

Building an ogive by hand

Class	Frequency	Upper boundary	Cumulative frequency
40–50	3	50	3
50–60	8	60	11
60–70	14	70	25
70–80	9	80	34
80–90	4	90	38

Plot (40, 0) to start, then (50, 3), (60, 11), (70, 25), (80, 34) and (90, 38), and join them. The last point always equals the total number of values.

Reading percentiles from the ogive

Median: half of 38 is 19. Going across from 19 meets the ogive in the 60–70 class, at about 65.7.
Quartiles: use n ÷ 4 = 9.5 for Q1 and 3n ÷ 4 = 28.5 for Q3. Their difference is the interquartile range.
“How many scored below 75?” Go up from 75 to the ogive and across: about 29.5 students.

The Statistics view under the chart lists the estimated median and quartiles exactly. For running totals as bars, use the cumulative frequency histogram; for the non-cumulative line, use the frequency polygon maker.

Common mistakes to avoid

Plotting at midpoints. Ogive points belong at the upper class boundaries.
Starting at the first point instead of zero. The ogive starts at (lower boundary of the first class, 0).
Reading the median at the wrong height. Use n ÷ 2 for counts (19 for n = 38), or 50% on a percentage ogive.

Do it in other software

Software	How
Excel	Make columns for upper boundary and running total, then insert a Scatter with straight lines.
Python	counts, edges = np.histogram(data, bins); plt.plot(edges, np.r_[0, counts.cumsum()], marker="o")
TI-84	Upper boundaries in L1, cumulative frequencies in L2, then an xyLine stat plot.

Frequently asked questions

What is an ogive?

An ogive (pronounced 'oh-jive') is a cumulative frequency graph. It plots the running total of frequencies against the upper boundary of each class and joins the points with straight lines, so the graph always rises from left to right.

How do I find the median from an ogive?

Switch the y-axis to Percent in the Bins tab. Go across from 50% to the ogive, then straight down to the x-axis. The value you land on is the median. Use 25% and 75% for the lower and upper quartiles.

Where does an ogive start?

At the lower boundary of the first class, with a cumulative frequency of 0, because no values lie below it. Each later point is at the upper boundary of a class.

What is the difference between a 'less than' and a 'more than' ogive?

A 'less than' ogive (the usual one, drawn here) shows how many values are below each upper boundary and rises. A 'more than' ogive shows how many values are above each lower boundary and falls. The two cross at the median.

Can I draw an ogive from a frequency table?

Yes. On the Data tab choose 'Frequency table' and enter each class with its frequency, such as '10-20: 4'. The ogive uses the class boundaries automatically.

Ogive Maker (Cumulative Frequency Graph)

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