In statistics, data can be measured on different scales, determining the type of analysis that can be performed on the data. The four most common measurement scales are nominal, ordinal, interval, and ratio (NOIR). Each scale has different properties and uses.

### 1. Nominal

Nominal scales do not have a meaningful zero point. Nominal scales classify data into distinct categories without any inherent order, so it doesn't matter which number comes first. For example, a nominal scale could classify people by gender (male or female) or political party (Democrat or Republican).

### 2. Ordinal

Ordinal scales are used to classify data into distinct categories that have a natural order. For example, an ordinal scale could be used to classify people by their level of satisfaction with a product (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied). Ordinal scales do not have a meaningful zero point, and the difference between them can not be quantified. So it is not possible to perform mathematical operations on the data. Still, it is possible to compare the relative order of the categories.

Another example of ordinal data would be Uber ride rating on a scale of 1 star to 5 stars.

### 3. Interval

Previously we talked about nominal and ordinal scales. Both of these scales had data in the form of categories.

Interval scales measure data on a continuous scale but without a meaningful zero point.

Interval and ratio scales of data are in the form of numbers, or we can say that these are numeric scales.

In the interval scale, we 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 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 "no temperature."

### 4. Ratio

Ratio scales are used to measure data on a continuous scale, with a meaningful zero point and the ability to compare ratios of different measurements. Ratio scales have a meaningful zero point and support the comparison of ratios, so it is possible to perform all mathematical operations on this type of data.

Examples of ratio scales 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.

# Appropriate Measurement of Central Tendency for NOIR Data

The measurement of central tendency is a statistical measure that describes a dataset's "typical" or "average" value. The most common measures of central tendency are the mean, median, and mode. These measures can be calculated for data measured on any of the four measurement scales.

### 1. Nominal

The mode is the most common measure of central tendency for nominal data. The mode is the value that occurs most frequently in the dataset and can be used to describe the typical or most common category of the data. For example, if a dataset contains the gender of 100 people, with 60 males and 40 females, the mode would be male because it occurs more frequently in the dataset.

### 2. Ordinal

For ordinal data, the mode and the median can be used as measures of central tendency. The mode is the value that occurs most frequently in the dataset, while the median is the value that splits the dataset into two halves. For example, if a dataset contains the level of satisfaction with a product for 100 people, with 20 very satisfied, 40 satisfied, 20 neutral, 10 dissatisfied, and 10 very dissatisfied, the mode would be "satisfied" because it occurs most frequently. The median also would be "satisfied" because it is the middle value of the dataset.

### 3. Interval and Ratio

For interval and ratio data, the mean, median, and mode can all be used as measures of central tendency. The mean is the arithmetic average of the data, calculated by summing all the values and dividing by the number of values. The median is the value that splits the dataset into two halves. The mode is the value that occurs most frequently in the dataset. For example, if a dataset contains the weights of 100 people in kilograms, with a mean of 75 kg, a median of 73 kg, and a mode of 76 kg, the mean, median, and mode would all be used to describe the typical or average weight of the people in the dataset.

Overall, the choice of measure of central tendency depends on the type of data being analyzed and the specific goals of the analysis. Different measures of central tendency can provide different insights into the data, and it is often helpful to calculate multiple measures of central tendency for the same dataset.

## Summary

To summarize, depending on 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 Ordinal data, you can use Mode or Median to measure central tendency.
- For Interval and Ratio scale, you can use any of three measurements of central tendency (Mean, Mode or Median).