Less-than cumulative frequency table
A less-than cumulative frequency table lists the number of observations less than each upper class boundary.
Practice This ConceptMain explanation
Teacher explanation
In this table, we keep adding frequencies and write totals against the upper limits of the classes. It is very useful for finding the median and for drawing ogives. The data becomes easier to interpret because the totals increase smoothly from top to bottom.
Example
For classes 0-10, 10-20, 20-30 with frequencies 4, 6, 5, the less-than cumulative frequencies are 4, 10, 15.
Simple analogy
Less-than means count up to the upper boundary.
Common confusion
Students sometimes attach the cumulative total to the lower boundary instead of the upper boundary.
Exam tip
Write the upper class boundary carefully; the graph and median position depend on it.
Answer writing and exam use
1-mark use
Write the exact meaning of less-than cumulative frequency table in one clean line.
2-mark use
Define less-than cumulative frequency table and add one example or condition.
3-mark use
Explain less-than cumulative frequency table, show the method or example, and mention the common mistake.
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