Explain the difference between the interquartile range and the range. Which is more sensitive to extreme values? Explain your thinking.

Interquartile range: Difference between the third and the first quartile.

Range: Difference between the highest and the lowest value of a dataset.

Since the range is not in the middle of a set (like the quartiles), it is more sensitive to extreme values.

Step-by-step explanation:

The interquartile range is the difference between the third quartile and the first quartile.

The first quartile (Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile (Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The range is the difference between the highest and the lowest value of a dataset.

Lets see two different sets of cardinality 8

Set 1: 5,5,6,7,8,9,13,13

Range = 13-5 = 8

Q1 = Element at the position 0.25*8 = 2 = 5

Q3 = Element at the position 0.75*8 = 6 = 9

IQR = Q3 - Q1 = 9 - 5 = 4

Now, replacing the first and the last element by extreme values

Set 1: 0,5,6,7,8,9,13,20

Range = 20-0 = 20

Q1 = Element at the position 0.25*8 = 2 = 5

Q3 = Element at the position 0.75*8 = 6 = 9

IQR = Q3 - Q1 = 9 - 5 = 4

The range changes and the IQR does not. Since extreme values are not in the middle of the distribution (in which the quartiles are), the range is more sensitive to extreme values, as this example showed.