## Scales of Measurement - Data types: Nominal, Ordinal, Interval and Ratio scale

There are four measurement scales:

- Nominal
- Ordinal
- Interval
- Ratio scale

Data measured on nominal and ordinal scale are called qualitative data while measured on interval and ratio scale are called quantitative data.

table, th, td { border: 1px solid; }Scale | Examples | Description | What is meaningful | Measure of central tendency |
---|---|---|---|---|

Nominal | Name, Gender, Pin code. | Denotes name or gender. Ordering is not possible. | Only count is meaningful | Mode |

Ordinal | Low, Medium, High. Rank 1st, 2nd, 3rd. | We can order the values. | Only ordering is possible. Not possible to measure the distance between values. | Median, Mode |

Interval | 1Year Temperature Celsius (°C). | 0°C does not mean there is no temperature. True zero absent. | Only difference is meaningful, but not the ratio | Mean, Median, Mode |

Ratio scale | Height, Weight. | True zero is present | Both difference and ratio are meaningful | Mean, Median, Mode |

Nominal data are just like labels. Gender such as male or female, name of a city or pin codes, they just denote a place or person or attribute. There is no other meaningful operation such ordering them, finding out the difference between cities or pin codes are not possible.

In ordinal scale, we can just order the values. For example, if a customer gives a ranking like high, medium and low preferences to different items, we can just rank these values saying that those values where a customer has expressed high preference has higher preference when compared to items where he marked medium or low. But here we cannot measure the distance between the rankings.

In interval scale, as there is no true zero, only difference is meaningful. For example, we can say that difference between year 2000 and year 3000 is 1000 years. But expressing in terms of ratio, i.e. the ratio of 3000 years is 1.5 times the year 2000 is meaningless. Here Year 0 doesn't mean there is no time. Year 0 is just a value. Hence in interval scale, there is no true zero. So only difference between values is meaningful.

Finally, the ratio scale. Examples such as height, weight where there is true zero. Height of 0 cm means there is no height, weight of 0 kg means there is no weight. Here both difference (he is 5 inches taller than me) and the ratio (he is 1.5 times taller than me) is meaningful.

Knowledge about scales of measurement is useful in choosing appropriate statistical tools for analysis and visualization.