Descriptive Statistics – Measures of Central Tendency - Quantiles

In the previous note, we have seen how to measure the central tendency using the Median. Mainly, it is a value in a frequency distribution that divides the total frequency into two equal parts. Now the question is why only two parts, why not three or four or more parts. In this section, we will try to get answers to the above question.

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Quantiles

Quantiles are the values that divide the frequency distribution into different partitions. These partitions can have equal or unequal widths, so in general, these partitions are called Quantiles and the partitions size is decided by us based on the requirements. For example:

25% Quantile: Splits the data into two parts such that at least 25% of the values are less than or equal to quantile, and at least 75% of the values are greater than or equal to quantile.
50% Quantile: Splits the data into two parts such that at least 50% of the values are less than or equal to quantile, and at least 50% of the values are greater than or equal to the quantile. It is also called Median.

Quartiles

The values which divide the given data into four equal parts, say, $Q_1, Q_2, Q_3, Q_4$ .

$Q_1$ : First quartile which has 25% of the observations.
$Q_2$ : Second quartile which has 50% of the observations also called Median.
$Q_3$ : Third quartile which has 75% of the observations.
$Q_4$ : Fourth quartile which has 100% of the observations.

We have divided the entire frequency distribution into four equal parts and these partitions are called as Quartiles and these are the partitions values of Quantiles.