There are four types of measurement scales used in statistics: nominal, ordinal, interval and ratio. Each scale has different properties and uses.
A nominal scale is category labels. The category labels are not ordered, so it doesn't matter which number comes first.
For example, the following list has three items on a nominal scale:
These three items are three categories of fruits. There is no order in this list. For example, you can not say that Banana is greater than Apple or Orange.
A nominal scale doesn't tell us anything about the relationship between the different categories. However, in the ordinal scale of data, there is an order. However, the difference between them can not be quantified.
For example, the following list has three ratings of a product on an ordinal scale:
These three items are categories, but they do have an order. However, we can not quantify the difference between the two values. The difference between Better and Good is not the same as the difference between Best and Better since these differences do not make any sense.
Another example of ordinal data would be Uber ride rating on a scale of 1 start to 5 stars.
Previously we talked about nominal and ordinal scales. Both of these scales had data in the form of categories.
Interval and ratio scale of data in the form of numbers or we can say that these two are numeric scales.
In the interval scale, we do have an order (just like ordinal data), and we can find the exact difference between the two values.
The classic example of an interval scale is the temperature in degrees Celcius. We can clearly say that 50 degrees C is greater than 40 degrees C. That means there is an order. We can also say that the difference between 50 and 40 degrees C is the same as the difference between 70 and 60 degrees C.
The only limitation of the interval scale is that there is no absolute or true zero. For example, 0 degrees C does not mean there is "no temperature."
The ratio scale has all the features of the Interval scale, and in addition, there is an absolute or true zero as well.
The examples of ratio scale include weight, height, volume etc.
We know that 10 Kg is greater than 5 Kg. The difference in weight between 10 Kg and 5 Kg is the same as the difference between 100 Kg and 95 Kg. Also, we do have an absolute zero here. A weight of 0 Kg means that there is no weight.
Measurement of Central Tendency
To summary a set of data, we use various measurements of central tendencies, such as Mean, Mode and Median.
Depending upon the measurement scales, you can use the most appropriate measure of central tendency.
- For Nominal data, use Mode as the measurement of central tendency.
- For Interval data, you can use Mode or Median as the measurement of central tendency.
- For Interval and Ratio scale, you can use any of three measurements of central tendency (Mean, Mode or Median).