# Construction of frequency distribution

Using the procedure in this lesson, and the quantitative raw data you see below, you will learn how to construct a frequency distribution table.

**Step 1:**

Pick 6 as the number of classes.

**Step 2: **Use the class width formula to find the class width.

Class width =

Class width =

Class width = = 10.166

Round 10.166 down to 10 and use 10 as a convenient number for the class width.

**Step 3:**

The lowest value in the list is 9. Let us use 9 as the lower limit of the first class.

To find the upper limit of the first class, subtract 1 from the class width and add the result to the lower limit of the first class.

10-1 =9

9 + 9 = 18

Therefore, the first class is 9-18

To find all the lower limits, just keep adding the class width to the previous lower limit.

**Lower limits (in bold)**

**9** + 10 = 19

**19** + 10 = 29

**29** + 10 = 39

**39** + 10 = 49

**49** + 10 =** 59**

**Upper limits (in bold)**

To find all the upper limits, just keep adding the class width to the previous upper limit.

**18** + 10 = 28

**28** + 10 = 38

**38** + 10 = 48

**48** + 10 = 58

**58** + 10 = **68**

All you need to do now is to count the frequency of these classes. For example, to know the frequency of 19-28, just count all the numbers between 19 and 20, starting with 19 and ending with 28.

Notice that the sum of all the frequencies is equal to 1 and the sum of all the percentages is equal to 100%

Income (In millions) |
Frequency |

9-18 |
12 |

19-28 |
9 |

29-38 |
7 |

39-48 |
8 |

49-58 |
7 |

59-68 |
7 |

Notice that the sum of all the frequencies is equal to 50.

**Relative frequency and percentage distribution.**

The relative frequency and percentage can be found using the same formula we used in this lesson.

The relative frequency of 9 for instance is = 0.18

To find the percentage, just multiply 0.18 by 100

0.18 × 100 = 18

The percentage is 18%

The table below shows the frequency distribution, the relative frequency, and the percentage distribution for the data set above.

Income (in millions) |
Frequency distribution |
Relative frequency |
Percentage |

9-18 |
12 | 0.24 | 24% |

19-28 |
9 | 0.18 | 18% |

29-38 |
7 | 0.14 | 14% |

39-48 | 8 | 0.16 | 16% |

49-58 |
7 | 0.14 | 14% |

59-68 |
7 | 0.14 | 14% |

Less than method for writing classes

Graphs of quantitative data