__Statistics Simplified __*is the series to express statistics in layman terms.*

Any data set should be analyzed for its __central tendency__ and variation. Why variation? What benefits will we get by looking at variation?

Let us consider this scenario: you have come across a river which can be crossed on foot as there is no bridge. You do not know swimming, and the current in the river is calm. There is a board at the river’s bank denoting the average depth as 3 feet.

You are 5.8 feet tall.

Will you cross the river?

In our day to day lives, we usually look at the average for performance comparison and decision-making.

It is a major flaw of our thought process as we ignore another critical aspect of data property: ** variation**.

And we call such thought process as “**Flaw of Averages**”.

Had there been additional details like maximum depth: 8 ft., then would you have crossed the river?

Considering the variation in the data helps in the wiser decision.

## What is the variation?

It is a measurement of the distance between the data points within a given data set.

## Measures of Variation

Popular ways to measure variations are Standard Deviation, Inter-Quartile Range (IQR), and Range.

· **Range**: Difference between maximum & minimum value.

· **Standard Deviation**: Average distance of data points from each other.

· **Inter Quartile Range (IQR)**: Difference between 75th percentile and 25th percentile, where percentile is the position of data points when arranged in an order. Median is the 50th percentile.

Also see: __Central Tendency __