How to calculate class width.

Group width can be calculated by working out the difference between the upper boundary and lower boundary of a group:

Class Width = Upper Boundary - Lower Boundary

If the frequency table contains discrete data values then this can be a little harder to work out (see example 2)

Class widths can be used when drawing a histogram, as the frequency density is equal to the frequency/class width. They are also useful if you need to use interpolation to find the lower quartile, median and upper quartile.

Example 1 - Continuous data

Class width example 1

The frequency table shows the finishing times of 20 athletes that took part in a race. Work out the class widths of all of the groups.

So all you need to do is work out the difference between the upper limit and lower limit of each group. The frequency column is not relevant to the question so it can be ignored.

The lower limit of the first group is 45 and the upper limit is 50, so the class width is 50 - 45 = 5.

The second groups with is 10 (since 60-50 = 10)

The lower boundary of the third group is 60 and the upper boundary is 80, so the width of this group is 80 - 60 = 20.

The final group has a group width of 5 (85 -80)

So the answers are 5, 10, 20 and 5 minutes.

Example 2 Discrete Data

Class width example 2

The frequency table shows the ages of a group of students who took part in a school play. Work out the group widths of each age group.

This time the data is discrete, so you have to think carefully where each group starts and ends. Again the frequency column is irrelevant.

The first group 0-4, starts on a lower limit of -0.5 and goes up to an upper limit of 4.5. So the width of this first class is 4.5 - - 0.5 = 5.

The second age range starts on a lower boundary of 4.5 and goes to an upper boundary of 9.5. So the group width is 9.5 - 4.5 = 5.

The third age range begins on a lower limit of 9.5 and goes to an upper limit of 12.5. So this group has a width of 12.5 - 9.5 = 3.

The final age group starts on a lower boundary of 12.5 and goes to an upper boundary of 16.5. So the width of this final group is 16.5 - 12.5 = 4.

So the class widths are 5, 5,3 and 4.

Class Width Summary

So to summarise the class width is the difference between the upper and lower boundary of the group.

If you found this article useful then check out my other math related pages. You will find many mathematical topics from the fields of algebra, number, geometry and statistics. All of these articles have been written in an easy to understand way. You will be shown easy to follow methods for solving simple equations, calculating averages from real life data, solving basic and advanced number problems involving fractions, percentages and ratio.

There will be also many other statistical topics coming up shortly, such as, how to draw a pie-chart and work out the angles, how to draw a stem and leaf diagram and work out the median and range from it, how to draw a cumulative frequency curve and calculate the lower quartile, the upper quartile and the median.

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