To find the frequency distribution of quantitative data, we can use the following table, which provides information on “Number of Smartphones Per Family”.

Raw data

For such quantitative data, it is quite easy to create a frequency distribution table.

People have either 1, 2, 3, 4, or 5 smartphones. Then all you have to do is find the frequency of 1, 2, 3, 4, and 5.

The frequency of 1 is 5.

The frequency of 2 is 20.

The frequency of 3 is 15

The frequency of 4 is 8

The frequency of 5 is 2

Finally, just put the information in a table.

Frequency distribution of quantitative data

As you can see there are 5 groups (1, 2, 3, 4 and 5). More precisely, we prefer to say 5 classes.

Group is the name we use for qualitative data.

There is nothing wrong with having less than 5 classes. Usually, however, the lowest number of classes is 5, and we like to use intervals for these classes.

Imagine you want to organize the data with only 3 classes. As you can see in the table below, we now have intervals for these classes. The first interval is 1-2.

The only problem is that using intervals cannot get at least 5 classes for this record.

Here, too, the classes must be intervals. However, if it is difficult to get at least 5 classes, it might be best to just do a frequency distribution with monovalent classes.

For single-valued classes, we can create a bar graph to show the data.

Quantitative data bar graph

Although we don’t usually have frequency tables with only 3 classes, I’ll use the table below to give you some important definitions.

Frequency distribution of quantitative data with classes

Lower class limits

1, 3 and 5 are referred to as the lower class limits.

Upper class boundaries

2, 4 and 6 are called upper limits.

3-4 is called the second grade. The upper limit of the third grade is 6.

Class boundary

The class boundary is the midpoint between the upper class boundary of one class and the lower class boundary of the next class.

For example, the class boundaries of the second class are 2.5 and 4.5.

4.5 is the midpoint between 4 and 5.

2.5 is the midpoint between 2 and 3.

We write 2.5 to less than 4.5

We call 2.5 the lower limit and 4.5 the upper limit.

Class breadth

Class width = upper limit – lower limit

In this example the class width = 4.5 – 2.5 = 2.

Make sure you can see the difference between cap and cap. For the same reason, don’t mix the lower limit with the lower limit.

Class center

The class center point, also known as the mark, is determined using the following formula.

Class center =

Lower limit + upper limit
/.
2

In our example, class center =

1 + 2
/.
2

= 1.5






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