1. Ogives
Year 8 ECHO Mathematics

2. Introduction
 An ogive is a way to graph information showing
cumulative frequencies.
 Your vertical scale will represent cumulative
frequencies and your horizontal scale will
represent upper class/interval boundaries.
 Ogives always start at the left with a cumulative
frequency of zero at the lower class boundary of
the first class.
 The ogive should end on the right with the
cumulative frequency equal to the sample size at
the upper class boundary of the last class.

3. Example one:
The following data consists of weights, in kilograms, of 20 people:
50, 65, 75, 80, 85, 85, 86, 86, 87, 87, 87, 90, 92, 98, 105.
Placing this data into a stem and leaf plot helps us organise and analyse
and group our data better. This is not a necessary step.
Step 1: Group your data into the table.
Stem
Tally
Leaf
5
0
6
5
40<weights<50
7
5
50<weights<60
8
0, 5, 5, 6, 6, 7, 7, 7
9
0, 2, 8
10
5
60<weights<70
70<weights<80
80<weights<90
90<weights<100
100<weights<110
Frequency
Cumulative
Frequency

4. Step 2: Put your data into
the table (Start with tallies)
Stem
Leaf
5
0
6
5
7
5
8
0, 5, 5, 6, 6, 7, 7, 7
9
0, 2, 8
10
5

5. Step 3: Put the frequencies
by which the events
occurred.
Stem
Leaf
5
0
6
5
7
5
8
0, 5, 5, 6, 6, 7, 7, 7
9
0, 2, 8
10
5

6. Step 4: Put in the cumulative
frequency
totals
Stem
Leaf
5
0
6
5
7
5
8
0, 5, 5, 6, 6, 7, 7, 7
9
0, 2, 8
10
5

7. Step 5: Draw your graph
• The first coordinate in the plot always starts at a
value of 0
• The second coordinate is at the end of the first interval.
• The third coordinate is at the end of the second interval and so on.