# What is the Extent of Variability? How Can You Measure It?

**Introduction**

Why do we need to know about the extent of variability? You might have worked on finding variability in your classes. But did you ever think about why you do that? The answer to this question is very simple. You want to understand the degree of data spread in a distribution. Measures of variability occur in the statistical studies frequently. You have to measure the extent of variability to know about the variety of the data. Today’s article is all about knowing the term variability in depth. Let’s begin discussing the topic with the following question:

**What Is The Extent Of Variability, And Why Do You Measure It?**

The measure of variability, sometimes called a dispersion measurement, is the descriptive information about the data spread. In distribution, the data is spread, and variability describes how far the data lies from the center. It helps in summarising the complete data.

While the average tells you where most information lies, the variability tells how far it is. It is crucial because, with the help of the extent of variability, you can tell how well generalized your results are. Low variability is ideal for dealing. You can better predict the information about the variables. High variability means that the data is less consistent, making it harder to make informed decisions.

**How To Measure The Variability?**

After knowing a bit about the variability and its use, let’s see how you can measure it. There are primarily four methods of measuring it. A brief description of all the methods along with the procedure and pros and cons is as follows as shared by experts of assignment writing services:

**Range**

The range is the easiest method to measure the extent of variability. It is the most straightforward method. The formula is so simple that even a student of class IV can find the range of the given distribution. It is based only on the two most extreme values.

**Procedure**

The procedure of the range is very simple. All you have to do is subtract the leftmost value from the rightmost value of the data. The resulting number after subtraction is the variability of the given information. See how easy it is to apply. For example, the leftmost value is 79, and the rightmost value in the dataset is 101. The variability by range method will be 101-79, equal to 22.

**Pros**

- An easy-to-use method that only involves subtraction
- It involves only two numbers to find the extent of the variability

**Cons**

- Only two outliners influence the variability
- It does not give any information about the distribution of values

**Interquartile range**

The second method of measuring the extent of variability is the interquartile range. It uses the middle half of the data. You have to divide the data into quarters similar to the median. Statisticians call these quarters quartiles or percentiles. They denote them from low to high as Q1, Q2, and Q3.

**Procedure**

The procedure for measuring variability from this method is as follows;

- First, you calculate the Q1, which contains the 25% values of the data
- In the second step, you calculate the Q4, i.e., the 25% of the higher values in the data
- The interquartile range (IQR) comes by subtracting Q3 from Q1

**Example**

Data (minutes): 52 110 134 190 238 287 305 215

Q1 position in the data: 0.25 x 8 = 2

Q3 position in the data: 0.75 x 8 = 6

After solving, Q1 is the value at the number second, which is 110, and Q3 comes out to be the 6^{th} value, i.e., 287.

IQR = Q3 – Q1

IQR = 287 – 110 = 177

**Standard Deviation**

Standard deviation is the most widely used and accepted method of measuring the extent of variability. It is the average of the variability in the dataset. It means that the standard deviation tells, on average, how far the data lies from the mean. Its relation with variability is directly proportional. The larger the standard deviation, the more variable the dataset has. The procedure to measure the standard deviation is as follows:

**Procedure**

- List each entry of the data in a column and find the mean of the data
- Subtract the mean from each entry to get the deviation
- Square each deviation to eliminate the negative sign
- Add up all the deviations
- Divide the above sum by n-1, where n is the number of total data sets
- Find the square root of the answer to the above step, and that is the standard deviation

**Pros**

- Rigidly defined, and the value is always fixed
- Based on all the entries, it is the best method

**Cons**

- A little complex to compute by hand as there are chances of errors in summation
- You cannot obtain a standard deviation for frequency deviation

**Variance**

The last and the most effective way of measuring the extent of variability is the variance. It is the average of the squared deviation from the mean. You can also say that it is the square of the standard deviation. It means that units of the variance are much larger than the actual dataset values. It is critical to calculate variance in statistical tests like ANOVAs when comparing different data sets.

**Procedure**

The procedure of calculating the variance is the same as the standard deviation. The only difference lies in the square. You square the standard deviation value after its calculation, and this is it. The formula of variance is below:

**Pros**

- It treats all the deviations regardless of their direction
- It gives useful insights into the data

**Cons**

- The units of the resulting number are very larger than the actual dataset
- It gives extra weight to the outliners in the data

**Conclusion**

Measuring the extent of variability is very easy if you know the right methods. The methods mentioned above have their own merits and demerits. The standard deviation is the most widely used and accepted of the above methods.