RANGE, INTERQUARTILE RANGE AND BOX PLOT

Range:

It is the difference between the highest and the lowest value. for example,

1. Range(team 1): 17.5 - 10.5 = 7

2. Range(team 2): 27.7 - 0 = 27.7

As ranges takes only the count of extreme values sometimes it may not give you a good impact on variability. In this case, you can go for another measure of variability called interquartile range (IQR).

Interquartile Range (IQR):

 It is a better measure of dispersion than range because it leaves out the extreme values. It equally divides the distribution into four equal parts called quartiles. First 25% is 1st quartile (Q1), last one is 3rd quartile (Q3) and middle one is 2nd quartile (Q2).

2nd quartile (Q2) divides the distribution into two equal parts of 50%. So, basically it is same as Median.

How 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.

Box Plot:

It is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum.

Consider two datasets:

A1={0.22, -0.87, -2.39, -1.79, 0.37, -1.54, 1.28, -0.31, -0.74, 1.72, 0.38, -0.17, -0.62, -1.10, 0.30, 0.15, 2.30, 0.19, -0.50, -0.09}

A2={-5.13, -2.19, -2.43, -3.83, 0.50, -3.25, 4.32, 1.63, 5.18, -0.43, 7.11, 4.87, -3.10, -5.81, 3.76, 6.31, 2.58, 0.07, 5.76, 3.50}