Question

1. Data with a z-score between the range of -2 to 2 is considered “usual” and data with a z-score outside of that range is considered “unusual.” Sort the following sample data into usual and unusual and justify your decision. You may use the fact that s = 2.4 5, 5, 4, 4, 6, 6, 10, 1, 4

Answer 1

Solution:

Given data set : 5, 4, 4, 6, 6, 10, 1, 4

n = 9

Mean = sum of observations/Number of observations

= (5 + 4 + 4 + 6 + 6 10 + 1 + 4)/9

= 5

Now , standard deviation of given data is given .

Standard deviation = 2.4

We know , z score of a observation x is given by

z score = (x - mean)/standard deviation

For first observation 5 ,

z score = (5 - 5)/2.4 = 0.00

Similarly we find z score for each observation.

Observation x	z score	Usual or Unusual
5	(5 - 5)/2.4 = 0.00	Usual
5	(5 - 5)/2.4 = 0.00	Usual
4	(4 - 5)/2.4= -0.42	Usual
4	(4 - 5)/2.4 = -0.42	Usual
6	(6 - 5)/2.4 = 0.42	Usual
6	(6 - 5)/2.4 = 0.42	Usual
10	(10 - 5)/2.4 = 2.08	Unusual
1	(1 - 5)/2.4 = -1.67	Usual
4	(4 - 5)/2.4 = -0.42	Usual