Range, Interquartile Range and Percentiles

Range(measures of variability):

The range of a set of data is the difference between the largest and smallest values.

Range might affect with Outliers like Mean.

Interquartile Range(measures of variability)

Interquartile range gives another measure of variability like Variance, Standard deviation.

It is a better measure of dispersion than range because it leaves out the extreme values(Outliers). It equally divides the distribution into four equal parts

Why I need IQR:

1. Let’s take two data sets and there Mean, Median and Mode are same, but there will be some variance in between two data sets in that case we will go for measures of variability like Range and IQR

Steps to Calculate IQR

Step 1: Order from low to high

Step 2: Find the median or in other words Q2

Step 3: Then find Q1 by looking the median of the left side of Q2

Steps 4: Similarly find Q3 by looking the median of the right of Q2

Steps 5: Now subtract Q1 from Q3 to get IQR.

Example:

Consider the below example to get clear idea.

Advantage of IQR:

• The main advantage of the IQR is that it is not affected by outliers because it doesn’t take into account observations below Q1 or above Q3 where Range will consider the outliers.
• It might still be useful to look for possible outliers in your study.

How to calculate Outliers using IQR:

As a rule of thumb, observations can be qualified as outliers when they lie more than 1.5 IQR below the first quartile or 1.5 IQR above the third quartile.

                                Lower Outliers = Q1 – 1.5* IQR   OR

                                Higher Outliers      =Q3 + 1.5*IQR

Percentiles:

Percentiles are commonly used in day to day life.For example in the test like the SAT, GRE and LSAT,the 70th percentile on the 2013 GRE was 156. That means if you scored 156 on the exam, your score was better than 70 percent of test takers.

The 25th percentile is also called the first quartile.
The 50th percentile is generally the median
The 75th percentile is also called the third quartile.
The difference between the third and first quartiles is the interquartile range.

For more information about percentiles please read in this link percentiles