Organisation of Data

How raw data are classified and grouped into frequency distributions, with class limits, class marks, widths, tally marks and the exclusive and inclusive methods.

Key ideas

Raw data are data as collected; classification arranges them into groups so that they are easy to compare and analyse.
Data can be classified chronologically (by time), spatially (by place), qualitatively (by attribute) or quantitatively (by size).
A continuous variable takes any value in a range (height); a discrete variable takes only certain values (number of children).
A frequency distribution shows how many observations fall in each class; a frequency array does this for a discrete variable.
In the exclusive method (10–20, 20–30) a value equal to an upper limit goes in the next class; in the inclusive method (10–19, 20–29) both limits belong to the class.
Grouping loses detail: each value is treated as if it were the class mark.

Remember

Class mark	(lower limit + upper limit) ÷ 2
Class width	upper limit − lower limit
Number of classes	(largest − smallest) ÷ class width
Tally marks	each bundle of five plus the single strokes: 5 × bundles + singles
Inclusive to exclusive	lower limit − 0.5 and upper limit + 0.5 (10–19 becomes 9.5–19.5)
Cumulative frequency (less than)	add the frequencies of all classes up to that one
Percentage frequency	class frequency ÷ total × 100

Watch out

Counting a value equal to the upper limit in the same class under the exclusive method.
Taking the class width as the class mark.
Calling the number of rooms continuous (it is discrete).

Worked example

Convert to the exclusive method: (a) 70–79 (b) 90–99. What is the width of each class?

Working: subtract 0.5 from the lower limit and add 0.5 to the upper

Answer: (a) 69.5–79.5, width 10 (b) 89.5–99.5, width 10