Question

Directions from assignment: Calculate the standard deviation for your data. Describe the range of values that are within 3 sigma of the mean and the impact it has on the likelihood of a value being in that range in terms of the variable chosen.

My data is : 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. I calculated the standard deviation as 4.3 and by using the calculated mean of 7.5. I do not know how to describel the range of values or what they are within 3 sigma of the mean of 7.5 and the impact it has on the likelihood of a value being in that range in terms of the variable chosen. If you could please help me out I would appreciate it. Thanks!

Answer 1

ol:

mean=7.5

X	XBAR	X-XBAR	(X-XBAR)^2
0	7.5	-7.5	56.25
1	7.5	-6.5	42.25
2	7.5	-5.5	30.25
3	7.5	-4.5	20.25
4	7.5	-3.5	12.25
5	7.5	-2.5	6.25
6	7.5	-1.5	2.25
7	7.5	-0.5	0.25
8	7.5	0.5	0.25
9	7.5	1.5	2.25
10	7.5	2.5	6.25
11	7.5	3.5	12.25
12	7.5	4.5	20.25
13	7.5	5.5	30.25
14	7.5	6.5	42.25
15	7.5	7.5	56.25
	TOTAL		340

X	XBAR	X-XBAR	(X-XBAR)^2
0	7.5	-7.5	56.25
1	7.5	-6.5	42.25
2	7.5	-5.5	30.25
3	7.5	-4.5	20.25
4	7.5	-3.5	12.25
5	7.5	-2.5	6.25
6	7.5	-1.5	2.25
7	7.5	-0.5	0.25
8	7.5	0.5	0.25
9	7.5	1.5	2.25
10	7.5	2.5	6.25
11	7.5	3.5	12.25
12	7.5	4.5	20.25
13	7.5	5.5	30.25
14	7.5	6.5	42.25
15	7.5	7.5	56.25
	TOTAL		340

sample standard deviation=sqrt(340/16-1)

=4.760952

Range of values lies within mean-3sd and mean+3d

mean-3*sd=7.5-3*4.760952= -6.782856

mean+3*sd=.7.5+3*4.760952=21.78286

All the sample data values lies within the range of  -6.782856 and 21.78286