Groups of information in statistics in form of qualitative or quantitative attribute of set of variables are referred as data. Data can be either grouped or ungrouped.

Ungrouped data is a rough data which have been just gathered and no further steps were performed on this data.

If the data is organized in groups, which are called classes, the data is referred to as grouped data. Each class has its own width, which is called the class interval. The correct selection of the class interval is very important. The width of each class interval could be equal or different depending on situation and on the way of how the data is grouped, but the size of the interval is always a whole number ^{[1]}.

In order to make class intervals in statistics the next steps should be accomplished ^{[2]}:

- The high and low scores should be determined and the range should be calculated, as follows:

**Range=High Score-Low Score**The group frequency distribution should be created; - The interval size should be selected and the number of intervals should be calculated as follows:
**Range/Interval size**; - The Apparent Limits should be selected (should be a multiple of Interval size). In order to select the lower apparent limits (LAL), the next conditions should be followed: all LAL should be a multiple of Interval size; select the closest multiple of Interval size to the highest score. In order to select the upper apparent limit (UAL) the next calculation should be performed: UAL (top interval)=LAL+i-1;
- The Apparent limits of the class intervals should be created.

**Problem #1.** The next data was obtained during an experiment:

48 | 55 | 95 | 45 | 46 | 72 | 77 | 66 | 53 | 42 |

47 | 46 | 45 | 32 | 73 | 94 | 99 | 75 | 56 | 35 |

56 | 67 | 67 | 67 | 68 | 67 | 88 | 68 | 68 | 37 |

78 | 86 | 83 | 58 | 77 | 76 | 77 | 45 | 67 | 48 |

Step 1. The high score is: 99; the low score is 32; Range=99-32=67;

Step 2. Since the Range is greater than 20, the group frequency distribution will be created;

Step 3. An interval size of 10 units was selected. Therefore number of intervals=67/10=6.7 (therefore there will be 7 intervals);

Step 4. The top LAL will be: 90; there the top UAL=90+10-1=99.

Step 5. The apparent limits of the class intervals are shown in the table below.

Apparent Limits |
---|

90-99 |

80-89 |

70-79 |

60-69 |

50-59 |

40-49 |

30-39 |

**Problem #2.** The next data was obtained after survey:

21 | 53 | 23 | 61 | 46 | 37 | 18 | 3 | 45 | 45 | 34 | 33 | 11 | 10 | 35 | 44 | 56 | 68 | 55 |

5 | 33 | 26 | 37 | 85 | 52 | 2 | 23 | 44 | 61 | 88 | 95 | 67 | 90 | 80 | 5 | 44 | 67 | 3 |

The next steps were accomplished to obtain class intervals for this problem:

Step 1. The high score is: 90; the low score is 2; Range=90-2=88;

Step 2. Since the Range is greater than 20, the group frequency distribution will be created;

Step 3. An interval size of 8 units was selected. Therefore number of intervals=88/8=11 (therefore there will be 12 intervals);

Step 4. The top LAL will be: 88; there the top UAL=88+8-1=95.

Step 5. The apparent limits of the class intervals are shown in the table below.

Apparent Limits |
---|

88-95 |

80-87 |

72-79 |

64-71 |

56-63 |

48-55 |

41-47 |

33-10 |

25-32 |

17-24 |

9-16 |

1-8 |

**References:**

[1] Statistical Data and Data Grouping | WyzAnt Resources. (2016). Wyzant.com. Retrieved 27 May 2016, from https://www.wyzant.com/resources/lessons/math/statistics_and_probability/introduction/data

[2] Worked Problem…..Class Intervals…..Psyc205/Soc205…..Vernoy. (2016). Daphne.palomar.edu. Retrieved 27 May 2016, from http://daphne.palomar.edu/stat/wpclassinterval.html

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