Please explain Consider the following three sets of sample o

Please explain:

Consider the following three sets of sample observations:

Set 1: 8, 9, 10, 11, 12

Set 2: 8, 9, 10, 11, 100

Set 3: 8, 9, 10, 11, 1000

Find the median and IQR for each data set.

Find the mean and standard deviation for each data set.

What do these data sets illustrate about the resistance of the median, IQR, mean, and standard deviation?

Solution

set1

set2

set3

n

5

5

5

mean

10.00

27.60

207.60

sample standard deviation

1.58

40.49

442.97

1st quartile

9.00

9.00

9.00

median

10.00

10.00

10.00

3rd quartile

11.00

11.00

11.00

interquartile range

2.00

2.00

2.00

What do these data sets illustrate about the resistance of the median, IQR, mean, and standard deviation?

When there is an extreme value or outlier, the median and IQR are not affected.

But when there is an extreme value, the mean and standard deviation are affected.

The mean and standard deviation is more affected by outliers than the median and IQR. The mean and standard deviation take every value in your data set into account, whereas the median only takes the position of the data into account.