Question

The depths​ (in inches) at which 10 artifacts are found are listed. 33.8  40.8  37.7  30.9  46.2  30.2  27.7  31.2  36.4  25.5   The range of the given data set is 20.7. If the current​ maximum, 46.2​, is replaced with 57.5​, the range then becomes 32.0. Compare these values and determine how outliers affect the range of a data set. How does changing the maximum value affect the​ range?

Answer 1

Step 1:

Given data values:

33.8, 40.8, 37.7, 30.9, 46.2, 30.2, 27.7, 31.2, 36.4, 25.5

Step 2:

Arranging data in ascending order, we get:

25.5, 27.7, 30.2, 30.9, 31.2, 33.8, 36.4, 37.7, 40.8, 46.2

Range = Maximum - Minimum = 46.2 - 25.5 = 20.7

So,

Answer is:

20.7

Step 3:

If current maximum, 46.2 is replaced by 57.5, the revised data set is:

25.5, 27.7, 30.2, 30.9, 31.2, 33.8, 36.4, 37.7, 40.8, 57.5

Range = Maximum - Minimum = 57.5 - 25.5 = 32.0

So,

Answer is:

32.0

Step 4:

Thus,

For data set without outlier = 57.5, Range = 20.7

For data set with outlier = 57.5, Range = 32.0

Thus,

outliers affect the range of a data set by increase of 20.7 to 32.0

Step 5:

Thus,

changing the maximum value affects the​ range to a great extent.