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### An introductory guide to calculating and using quartiles

Read our short guide on what quartiles are, how they work in statistical and data analysis, and how to calculate them for your dataset.

As a business owner, if you are dealing with statistical formulas, you may have come across quartiles. These can be useful many statistical formulas can be used to divide data points or groups of observations. Keep reading for our guide on what quartiles are, how they work, and how to calculate them.

## Definition of a quartile

A quartile, a statistical term, is used to divide a data set into four groups (or intervals). The groups are based on data values and their relation to the whole data set. To organise data points into quartiles, they need to be plotted on a number line and listed in ascending order. You then divide them into four quartiles.

## How quartiles work

To comprehend quartiles, it is crucial to talk about the median. The media is the middle value of any set of numbers. At the median, half of the number of data points lie above and below the central number (or median). Quartiles work along the same principle and take it one step further by measuring the spread or distribution of values both above and below (upper and lower quartiles) the middle point.

The first quartile, or lower quartile (Q1), works as follows: The lowest 25% of data is separated from the highest 75%. This is the middle number between the median and the dataset’s smallest value.

The second quartile and third quartile, or middle quartiles, work as follows (Q2): These are the same as the median of the data set, including the two middle sections of the data set – 50% of the data is less than the median.

The fourth quartile, or upper quartile (Q3): This includes the highest data points and separates the highest 25% of data points from the lowest 75%. This is the central point between the median and the highest number of the set.

Interval 1 encompasses the smallest value up to Q1, interval 2 Q1 up to the median, Interval 3 the median to Q3, and Interval 4 Q3 to the highest value.

## Calculating quartiles

For smaller data sets, you can simply calculate the quartiles. If you had 'N' number of data points, the formulas for the quartiles would look as follows:

Lower Quartile (Q1) = (N+1) * 1/4

Middle Quartile (Q2) = (N+1) * 2/4

Upper Quartile (Q3) = (N+1) * 3/4

## Quartiles in large datasets

When working with large sets of data, it is generally easier to make use of the QUARTILE function in Microsoft Excel. This function can be found under Excel's 'Statistical Functions'. You simply need to fill in the set of values into the box and the program will return the quartile. When plugged into a cell in a worksheet, the function can provide you with the minimum value, first, second and third quartile, and maximum value.

In practice, quartiles can help break down eg revenues or inventory sales by providing you with more manageable pieces of datasets.

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