# Less than method for writing classes

The less than method for writing classes is used for data sets that contain fractional values or continuous variables such as the ones in table 1.

We will construct a frequency table and then calculate the relative frequencies and the percentage for all classes.

Choose 5 as the number of classes.

Class width =

Class width = = = 2.8

The class width can be approximately 3. We can use 1 as the lower limit of the first class.

The upper limit of the first class has to be 4

1-4

4-7

7-10

10-13

13-16

Notice that the **upper** limit of one class is also the **lower** limit of the next class.

This is different from the way we did it for discrete variables. For discrete variables, your classes will look more like option #1.

However, option #1 does not include values between 3 and 4 such as 3.4

Therefore, the upper limit of one class has to be the lower limit of the next class to make sure that all values are included.

Option #2 includes all values. However, it has 7 classes as opposed to 5.

**Option #1**

1-3

4-6

7-9

10-12

13-15

**Option #2**

1-3

3-5

5-7

7-9

9-11

11-13

13-15

The **proper** way to write the classes though is like this.

1 to less than 4

4 to less than 7

7 to less than 10

10 to less than 13

13 to less than 16

To find the frequency of the first class, just count how many numbers are between 1 and 4 starting with 1 and ending with a number less than 4

To find the frequency of the second class, just count how many numbers are between 4 and 7 starting with 4 and ending with a number less than 7

And so forth.

The frequency table is shown below along with the relative frequency and the percentage.

Time (in seconds) |
Frequency distribution |
Relative frequency |
Percentage |

1 to less than 4 |
12 | 0.4 | 40% |

4 to less than 7 |
7 | 0.2333 | 23.33% |

7 to less than 10 |
5 | 0.1666 | 16.66% |

10 to less than 13 | 4 | 0.1333 | 13.33% |

13 to less than 16 |
2 | 0.066 | 6.66% |

To calculate the relative frequency of the first class, just divide 12 by 30.

To Find the percentage of the first class, just multiply the relative frequency by 100

To calculate the relative frequency of the second class, just divide 7 by 30.

To Find the percentage of the second class, just multiply the relative frequency by 100

and so forth.

Construction of frequency distribution

Graphs of quantitative data