This tutorial explains the types of data in statistics, such as Interval, Nominal, Ordinal data.

You may also want to read:

Excel Range, Variance, Standard Deviation

Excel central tendency (mean mode median)

## Types of data in statistics (Interval, Nominal, Ordinal)

This tutorial is nothing related to Excel, but it is the foundation for my other Excel statistics tutorial.

Understanding the data type is the first step to understand statistics, because it affects what data we should collect in a survey.

#### Interval Data / Quantitative Data / Numerical Data / Ratio Data

These type of data are numeric values that can be used directly for calculation.

For example, 3 students have test marks of 50, 60, 70.

Name of Student | Marks |

John | 50 |

Mary | 60 |

Peter | 70 |

Since marks are numerical, you can directly do calculation on the marks.

#### Difference between Ratio Data and Interval Data

There is a difference between Ratio and Interval Data although we don’t need to define that in statistical software.

Interval Data has an arbitrary zero point (no true zero point). For example, a person of IQ 160 does not mean he is cleverer than those IQ 80 twice.

Ratio Data has a nature zero point. For example, $10,000 salary is twice of $5000.

#### Nominal Data / Qualitative Data / Categorical Data

These type of data are text values cannot be used for calculation, it is used for grouping the same kind of data together.

In Excel, we can imagine we group nominal data using Pivot Table, and then apply aggregate Function on numerical data such as count (in statistics we call it frequency)/ sum / average (mean) / max / min.

For example, 3 students have two tests in the year.

Name of Student | Test | Marks |

John | Semester 1 | 50 |

Mary | Semester 1 | 60 |

Peter | Semester 1 | 70 |

John | Semester 2 | 40 |

Mary | Semester 2 | 50 |

Peter | Semester 2 | 55 |

Now we can group the student name (nominal data) and then apply average on marks (numerical data).

Name of Student | Average of Marks |

John | 45 |

Mary | 55 |

Peter | 62.5 |

#### Ordinal Data

Some nominal data has rank. For example, instead of giving students a mark, the result can be a grade. Student Name is not ordinal data because it has no rank.

Name of Student | Grade |

John | A |

Mary | B |

Peter | C |

Because we cannot perform calculation on grade, we need to convert grade to a numerical value. We make up a mapping table as below, assume that difference between each grade are the same.

Grade | Marks |

A | 5 |

B | 4 |

C | 3 |

D | 2 |

E | 1 |

Now we can perform analysis such as mean, average, median. The average of the mark is 4, which means average grade is B.

Name of Student | Marks |

John | 5 |

Mary | 4 |

Peter | 3 |

Theoretically ordinal data should not be used to calculate mean (because the value between each ordinal group could be different), therefore ordinal data cannot be used in correlation, t-test, ANOVA. However, academic convention allows us to do so with understanding of the error caused.