Types & Scales of Data in Descriptive Statistics

Descriptive statistics help you to understand the data, but before we understand what data is, we should know different data types in descriptive statistical analysis. The below screen helps you to get an overview of it.

Types of Data

A data set is a grouping of information that is related to each other. A data set can be either qualitative or quantitative. A qualitative data set consists of words that can be observed, not measured. A quantitative data set consists of numbers that can be directly measured. Months in a year would be an example of qualitative, while the weight of persons would be an example of quantitative data.

Now, let’s suppose you go to KFC to eat some burgers along with your friends, you placed the order at coupon counter and after receiving from the food counter everyone eats what you ordered on their behalf. If someone asked about the taste to others then the ratings on the taste will vary from one to another but if asked how many burgers we ordered then everyone will come to a definite count and it will be the same for all. Here, Taste’s ratings represent the Categorical Data and the number of burgers is Numerical Data.

Types of Categorical Data:

1. Nominal Data: When there is no natural order between categories then data is nominal type.
   Example: Color of an Eye, Gender (Male & Female), Blood Type, Political Party, and Zipcode, Type of living accommodation(House, Apartment, Trailer, Other), Religious preference( Hindu, Buddhist, Muslim, Jewish, Christian, Other), etc.
2. Ordinal Data: When there is natural order between categories then data is ordinal type. But here, the difference between the values in order does not matter.
   Example: Exam Grades, Socio-economic status (poor, middle class, rich), Education-level (kindergarten, primary, secondary, higher secondary, graduation), satisfaction rating(extremely dislike, dislike, neutral, like, extremely like), Time of Day(dawn, morning, noon, afternoon, evening, night), Level of Agreement(yes, maybe, no), The Likert Scale(strongly disagree, disagree, neutral, agree, strongly agree), etc.

Types of Numerical Data:

1. Discrete Data: The data is said to be discrete if the measurements are integers. It represents count or an item that can be counted.
   Example: Number of people in a family, the number of kids in class, the number of cricket players in a team, the number of cricket playing nations in the world.
   Discrete data is a special kind of data because each value is separate and different. With any data, if we can answer the below questions then it is discrete.
   1. Can you count it?
   2. Can it be divided into smaller and smaller parts?
2. Continous Data: The data is said to be continuous if the measurements can take any value usually within some range. It is a scale of measurement that can consist of numbers other than whole numbers, like decimals and fractions.
   Example: height, weight, length, temperature
   Continuous data usually require a tool, like a ruler, measuring tape, scale, or thermometer, to produce the values in a continuous data set.

Scales of Measurement:

Data can be classified as being on one of four scales: nominal, ordinal, interval or ratio. Each level of measurement has some important properties that are useful to know.

1. Nominal Scale: Nominal datatype defined above can be placed into this category. They don’t have a numeric value and so it neither be added, subtracted, divided nor be multiplied. They also have no order; if they appear to have an order then you probably have ordinal variables instead.
2. Ordinal Scale: Ordinal datatype defined above can be placed into this category. The ordinal scale contains things that you can place in order. For example, hottest to coldest, lightest to heaviest, richest to poorest. So, if you can rank data by 1st, 2nd, 3rd place (and so on), then you have data that is on an ordinal scale.
3. Interval Scale: An interval scale has ordered numbers with meaningful divisions. Temperature is on the interval scale: a difference of 10 degrees between 90 and 100 means the same as 10 degrees between 150 and 160. Compare that to Olympic running race (which is ordinal), where the time difference between the winner and runner up might be 0.01 second and between second-last and last 0.5 seconds. If you have meaningful divisions, you have something on the interval scale.
4. Ratio Scale: The ratio scale has all the property of interval scale with one major difference: zero is meaningful. When the scale is equal to 0.0 then there is none of that scale. For example, a height of zero is meaningful (it means you don’t exist). The temperature in Kelvin(0.0 K), 0.0 Kelvin really does mean “no heat”. Compare that to a temperature of zero, which while it exists, it doesn’t mean anything in particular (although admittedly, in the Celsius scale it’s the freezing point for water).

Scales of Measurement

Note: When working with ratio variables, but not interval variables, the ratio of two measurements has a meaningful interpretation. For example, because weight is ratio variable, a weight of 4 grams is twice as heavy as a weight of 2 grams. However, a temperature of 10-degree celsius should not be considered as hot as 5-degree celsius. In that case, a conflict would be created because 10-degree Celsius is 50-degree Fahrenheit and 5-degree Celsius is 41-degree Fahrenheit. Cleary 50-degree is not twice as 41-degree.