1.05 Range, Interquartile Range and Box Plot

Question 1

RANGE

Answer 1

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

The range is a measure of variability that is:

• easy to understand
• simple to compute.

However, in many cases it doesn’t give a good impression of the variability of the data. The reason is that it only takes into account the extreme values.

Question 2

INTERQUARTILE RANGE

Answer 2

Another measure of variability, the interquartile range, is a better measure of dispersion because it leaves out the extreme values.

It basically divides your distribution in four equal parts. After all, 50% of the values is below Q2 this value and 50% lies above the value. Q2 is therefore the same as the median. The Q1 is the middle of the left half, the Q3 is the middle of the right half.

IQR = Q3- Q1

The interquartile range is the distance between the third and the first quartile, or in other words.

Question 3

BOX PLOT

Answer 3

A box plot shows important aspects of a distribution in a compact way, using three quartiles (Q1, Q2, Q3) , the outliers, and the range of the data after removing the outliers.