Question

I need help with deviation questions.

My data:

8
2
2
5
8
6
2
3
5
7
5
2
2
2
5
4
8
1
2
1
1
5
1
5
5
0
0
7
7
11
5
9
3
2
5
2
5
1
4
3
5
3
4
3
7
7
6
1
0
3
2
6
4
1
1
4
4
4
5
0
5
4
1
7
3
3
3
0
5
2
4
2
3
4
2
2
3
3
5
4
1
7
6
3
3
2
1
5
7
2
1
2

The mean of this data is 3.65217391 and the standard deviation is 2.30839742

The questions:

1. Compare the first value of your data (8) to the mean (3.6521..)

* Is this value within ONE standard deviation of the mean? Is it beyond one standard deviation of the mean? Is it more than two standard deviations from the mean but within three?

* Are there any values that are more than three standard deviations from the mean? (Identify the limits of this range, state 'yes' or 'no' and identify the values if there are any.)

Answer 1

1.

Mean = 3.65217391

Std. Deviation = 2.30839742

X = 8

Std. variable = (X-mean)/Std. Deviation

= 1.88

Thus,

Is this value within ONE standard deviation of the mean? = No

Is it beyond one standard deviation of the mean? = Yes

Is it more than two standard deviations from the mean but within three? = No

Mean3*std. deviation = 3.65217391 3*2.30839742

= [-3.273,10.5774]

Yes

11

Please upvote if you have liked my answer, would be of great help. Thank you.