Question

For each part create two different data distributions ( data sets ) having the specified properties by choosing nine values from the set {1, 2, 3, 4, 5} and construct a histogram of each of your two distributions.

a- The two distributions have equal means but different standard deviations.

b- The two distributions have different means but equal standard deviations.

c- The two distributions have equal means and equal standard deviations (but the means need not equal the standard deviations)

Answer 1

a) example of such distributions

	Dist 1	Dist 2
	2	1
	2	1
	2	1
	2	1
	2	2
	2	3
	2	3
	2	3
	2	3
Mean	2	2
SD	0	0.942809

b) different means but equal standard deviations:

	Dist 1	Dist 2
	1	2
	1	2
	1	2
	1	2
	2	3
	3	4
	3	4
	3	4
	3	4
Mean	2	3
SD	0.942809	0.942809

c) equal means and equal standard deviations and mean not equal to SD

	Dist 1	Dist 2
	1	1
	1	1
	1	1
	1	1
	2	2
	3	3
	3	3
	3	3
	3	3
Mean	2	2
SD	0.942809	0.942809