Intuition of Variance and Standard Deviation

Standard Deviation and Variance are parameters used to see how messy a dataset is. How far the data points spread from their average

According to the quote above, these two parameters are indeed used as indicators of how messy a dataset is. Messy here can be interpreted as the data points being far apart

If you're still confused, just look at the illustration below

In reality, in terms of average, they are both 80. But in Class B, there are two people who scored below the standard, namely 60, while Class A is entirely above standard. If the mean is the same at 80, the correct way to interpret it is using Variance and Standard Deviation.

How to Measure Variance and Standard Deviation

Variance

Variance measures how far each data point is from the average value.

The formula looks a bit scary!

Maybe those who see the formula above will ask this:

The answer is simple:

1. So that all values become positive.

2. So that larger deviations get greater weight.

Still confused? Look at the data below

Without squaring, even if there are data points that have a distance from the mean, when summed they can cancel each other out, resulting in a variance of 0. To prevent that from happening, variance is squared.

Standard Deviation

Standard deviation is a measure of data dispersion, but its unit is the same as the original data.

Yes, unfortunately the variance value has a different dimension from the original data. For example:

• Height → cm²

• Salary → rupiah²

Hard to imagine, right?

From there came the concept of standard deviation, so that the spread value is easier to understand

This means that in this company, employees' salaries differ by only about 3 million from the average. For example, if the average salary is 10 million, then the salary of an employee named Bahlil might be ± Rp3 million from the average.

The formula is simple

When should you use Variance and Standard Deviation?

Okay, let's move to the main menu that confuses many people. Both explain the spread of data relative to the mean. So when should you use variance and when should you use standard deviation?