Organise individual values or grouped intervals while preserving clear class boundaries.
Counts make the data easier to work with
An ungrouped frequency table lists each distinct value and its frequency f. It retains the original numerical values. A grouped table counts observations in intervals; it is compact for many continuous measurements but loses the exact values within each class.
The total frequency is n=∑f. A cumulative frequency (CF) is a running total and helps locate ordered observations.
Make interval membership unambiguous
Classes such as 10≤t<20 and 20≤t<30 place a value of exactly 20 in the second class. For continuous measurements, use adjoining boundaries without gaps.
Rounded measurements
Values recorded as 10–19 to the nearest whole unit represent 9.5≤x<19.5.
Truncated measurements
Completed ages 10–19 represent 10≤x<20. The recording convention changes the boundaries.
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Take the same fraction of the class width
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05•Data Presentation & Measures
Range & Interpercentile Ranges
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