When working with larger data sets, it is often helpful to group data into class intervals. This applies to both discrete and continuous data and makes patterns and trends easier to see.

 

 

What Class Intervals Are

Class intervals are ranges of values used to group data.

 

Instead of listing every individual value, values are placed into intervals such as 0–9, 10–19 and 20–29.

 

Each data value must fall into one interval only.

 

Class intervals are commonly used when:
• there are many different values
• the data range is large
• the data is continuous

 

 

Grouping Discrete Data

Discrete data consists of separate, distinct values.

 

Examples include number of goals scored or number of books owned.

 

Discrete data can be grouped into class intervals when there are many possible values.

 

For example, a data set of test scores could be grouped as:
• 0 to 9
• 10 to 19
• 20 to 29

 

Each value is counted once and placed in the appropriate interval.

 

 

Grouping Continuous Data

Continuous data can take any value within a range.

 

Examples include height, mass and time.

 

Continuous data is almost always grouped into class intervals.

 

When grouping continuous data:
• intervals should cover the entire range
• intervals must not overlap
• boundaries should be clear

 

For example, heights might be grouped as:
• 140 to less than 150
• 150 to less than 160
• 160 to less than 170

 

This avoids ambiguity about where values belong.

 

 

Equal Width Class Intervals

Equal width intervals all have the same size.

 

For example:
• 0 to 10
• 10 to 20
• 20 to 30

 

Equal width intervals are easier to work with and are often preferred, especially when drawing graphs.

 

They make comparisons between groups clearer.

 

 

Unequal Width Class Intervals

Unequal width intervals have different sizes.

 

For example:
• 0 to 5
• 5 to 20
• 20 to 50

 

These may be used when:
• data is unevenly spread
• more detail is needed in one part of the data
• values cluster in a particular range

 

Extra care is needed when interpreting graphs drawn from unequal intervals.

 

 

Choosing Appropriate Intervals

When choosing class intervals:
• consider the range of the data
• choose intervals that include all values
• avoid intervals that are too wide or too narrow

 

Intervals that are too wide hide detail.
Intervals that are too narrow make patterns hard to see.

 

The choice of intervals affects how the data appears

 

 

Common Errors to Avoid

Common mistakes include:
• overlapping intervals
• leaving gaps between intervals
• placing values into more than one interval
• mixing equal and unequal widths without reason

 

Clear definitions prevent these errors.

 

 

Key Points to Remember

Class intervals group data into ranges.
Discrete and continuous data can both be grouped.
Equal width intervals are easier to compare.
Unequal width intervals may be used when needed.
Intervals must not overlap and must cover all data values.

 

Grouping data into suitable class intervals makes large data sets clearer and supports accurate statistical analysis.