How To Find Interquartile Range On Box Plot

Let's recall, in sure cases, you lot are comparing two groups. You have already calculated the central trend of your information i.e. Mean, Median and Mode for both the groups. Sometimes it may happen that mean, median, and mode are same for both groups. Permit's take the below example:

If y'all consider both the team their Fashion= xiv.1, Median=15 and Mean=xv

This indicates that, if you adequately describe a distribution some time information technology may need more data than the measures of key tendency.

In this situation measures of variability comes into picture. They are

Range
Interquartile range.
Box Plot to get proficient indication of how the values in a distribution are spread out.

Range:

The most simple mensurate of variability is the range. It is the difference between the highest and the lowest value.

For the above Example range will be:

Range(team1) = 19.3 – 10.8 = 8.5

Range(team2) = 27.seven-0 = 27.7

As ranges takes merely the count of extreme values sometimes information technology may non requite you a skilful impact on variability. In this case, you can go for another measure of variability called interquartile range (IQR).

Interquartile Range (IQR):

Interquartile range gives some other measure of variability. Information technology is a improve measure of dispersion than range because it leaves out the extreme values. It equally divides the distribution into four equal parts called quartiles. Get-go 25% is 1^st quartile (Q1), final i is 3^rd quartile (Q3) and middle 1 is 2^nd quartile (Q2).

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

The interquartile range is the distance between the third and the first quartile, or, in other words, IQR equals Q3 minus Q1

IQR = Q3- Q1

How to calculate IQR

Step i: Social club from low to high

Step 2: Find the median or in other words Q2

Pace 3: And then find Q1 past looking the median of the left side of Q2

Steps four: Similarly notice Q3 by looking the median of the right of Q2

Steps v: At present subtract Q1 from Q3 to get IQR.

Example:

Consider the below case to become clear idea.

Consider another example to get better agreement.

Consider the following numbers: 1, 3, 4, 5, v, 6, 7, xi. Q1 is the middle value in the first half of the data set. Since there are an fifty-fifty number of data points in the get-go one-half of the data set, the middle value is the average of the ii middle values; that is, Q1 = (3 + 4)/2 or Q1 = iii.v. Q3 is the middle value in the second half of the data gear up. Once more, since the second half of the data prepare has an fifty-fifty number of observations, the eye value is the average of the two middle values; that is, Q3 = (6 + vii)/2 or Q3 = 6.5. The interquartile range is Q3 minus Q1, so IQR = 6.5 – 3.v = 3.

Advantage of IQR:

The main advantage of the IQR is that it is not afflicted by outliers because it doesn't take into account observations beneath Q1 or higher up Q3.
It might withal be useful to look for possible outliers in your study.
As a dominion of thumb, observations tin be qualified as outliers when they lie more ane.5 IQR beneath the get-go quartile or 1.5 IQR to a higher place the third quartile.

Outliers = Q1 – 1.v* IQR OR

=Q3 + i.5*IQR