Question

Create a small dataset of at least 5 observations and calculate the mean, median, mode, range, IQR and standard deviation (use Excel or StatCrunch). Add an outlier to your data and recalculate these measures. Which changed and by how much? Explain how this illustrates the idea of resistant measures. Please provide the data that you made up and the measures for your data before and after you added an outlier. Organizing the data into a table would be a great way to display all of this

Answer 1

Solution:

Let five numbers given as below:

X

5

8

12

14

16

The required descriptive statistics by using excel are given as below:

X
Mean	11
Median	12
Mode	#N/A
Standard Deviation	4.47
Range	11
Minimum	5
Maximum	16
Sum	55
Count	5
First Quartile	6.5
Third Quartile	15
IQR	8.5

Now, we have to add one outlier in this data. Suppose we add an outlier as 49 in this data. So data becomes as below:

X

5

8

12

14

16

49

Now, we have to find the above descriptive statistics for this data including outlier. The required descriptive statistics are given as below:

X
Mean	17.33
Median	13
Mode	#N/A
Standard Deviation	16.02
Range	44
Minimum	5
Maximum	49
Sum	104
Count	6
First Quartile	8
Third Quartile	16
IQR	8

Now, we have to compare the values of descriptive statistics. The comparisons for these descriptive statistics are given as below:

Statistics	Original Data	Data with outlier	Comparison
Mean	11	17.33	There is a large difference.
Median	12	13	There is a small difference.
Mode	#N/A	#N/A	#N/A
Standard Deviation	4.47	16.02	There is a large difference.
Range	11	44	There is a large difference.
Minimum	5	5	There is no difference.
Maximum	16	49	There is a large difference.
Sum	55	104	There is a large difference.
First Quartile	6.5	8	There is a small difference.
Third Quartile	15	16	There is a small difference.
IQR	8.5	8	There is a small difference.

So, it is observed that the first quartile, median or second quartile, third quartile, and IQR (Interquartile range) is more effective if data contains an outlier.