As always starting with link to the previous articles
Measures of spread
Have a look at the below samples and its mean, median
Sample1: 81,81,82,82,83,83,84,84,85,85
Mean: 83
Median:83
Sample2: 31,41,61,72,83,83,94,105,125,135
Mean: 83
Median:83
The mean and median are same for both the samples. If you look closely on each of the sample data, the first sample has less spread of values whereas in second sample the values has more variability and spread. Clearly the mean and median doesn't give a clear picture of on Measures of spread.
Let calculate the range:
Sample1 : 85–84=4
Sample2: 135–31 = 104
The range helps us to describe that second sample has more more variability and spread.
Lets add 1 additional data in our sample 1 :
Sample1: 81,81,82,82,83,83,84,84,85,85,335
now if we calculate the range = 335–81 =254
Though the range is correct, it doesn't give a clear picture as one outlier increases the range value.
The best way to solve it is by calculating Inter Quartile Range(IQR)
IQR = Q3 — Q1
Q3 or L 75th = 75/100 *( 11+1) = 9th element = 85
Q1 or L 25th = 25/100 *(11 + 1) =3rd element = 82
IQR = 85–82 = 3
Though the range is 254 , the IQR is 3. The IQR gives a clear picture that it is not sensitive to Outlier, whereas range is sensitive to IQR
