Grouped Frequency Distribution Calculator

You can use this grouped frequency distribution calculator to identify the class interval (or width) and subsequently generate a grouped frequency table to represent the data.

How to use the calculator: Enter the data values separated by commas, line breaks, or spaces. Enter the details of the required number of intervals, and click on the "Calculate" button.

Class Intervals

It can be useful to group data into class intervals when the frequency table has become large. Class intervals enable us to more readily present, interpret, and assess the data. The class interval frequency is the number of data values that fall within the range stipulated by the interval. It is sometimes referred to as the class width.

The class interval represents the distance between a given class' lower class limit and the lower class limit of the next class. As described above, all the class intervals within a frequency distribution must be of equal width.

The formula for determining class intervals is as follows:

i ≥ (H − L) / k

Where:

i is the class interval,

H is the greatest observed value,

L is the smallest observed value,

k is the number of class intervals.

Generally, 5 ≤ k ≤ 15. You can use Sturges' rule as a guide:

k = 1 + 3.322 log₁₀ (n) , where n = number of observations.

The inclusion of the greater than or equal sign, ≥, indicates that it may be necessary to round the outcome of the equation up to the next integer. It is vital that you round up, and not down. As such, while you may typically round the number 3.3 down to 3 in alternative contexts, when calculating class intervals, you need to round up. As such, 3.3 would become 4.