Question

If upper quartile is 1175 and lower quartile is 900 then inter quartile range is ?​

Answer 1

The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). So, it gives you an idea about the range within which the central 50% of your sample data lies. Consequently, based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Since both of these topics are based on the concept of quartiles, we’ll first understand how to calculate the quartiles of a dataset before working with the direct formulae.

A median divides a given dataset (which is already sorted) into two equal halves similarly, the quartiles are used to divide a given dataset into four equal halves. Therefore, logically there should be three quartiles for a given distribution, but if you think about it, the second quartile is equal to the median itself! We’ll deal with the other two quartiles in this section.

• The first quartile or the lower quartile or the 25th percentile, also denoted by Q1, corresponds to the value that lies halfway between the median and the lowest value in the distribution (when it is already sorted in the ascending order). Hence, it marks the region which encloses 25% of the initial data.
• Similarly, the third quartile or the upper quartile or 75th percentile, also denoted by Q3, corresponds to the value that lies halfway between the median and the highest value in the distribution (when it is already sorted in the ascending order). It, therefore, marks the region which encloses the 75% of the initial data or 25% of the end data.