Question

Consider a sample with six observations of 11, 6, 9, 15, 15,16 and calculate z score. Consider another sample with 10 observations of 15, –1, 7, 0, 1, 13, 3, 9, 14, and –3. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution.

What can be said about the 2 data sets

Answer 1

### By using Excel:

	X	X-Xbar	Z=(X-Xbar)/sd		Y	Y-Ybar	Z=(Y=Ybar)/sd
	11	-1	-0.25		15	9.2	1.37
	6	-6	-1.5		-1	-6.8	-1.01
	9	-3	-0.75		7	1.2	0.18
	15	3	0.75		0	-5.8	-0.87
	15	3	0.75		1	-4.8	-0.72
	16	4	1		13	7.2	1.07
Total	72				3	-2.8	-0.42
					9	3.2	0.48
xbar	12				14	8.2	1.22
sd	4				-3	-8.8	-1.31
				Total	58
				Ybar	5.8
				sd	6.7

using formula:

Xbar =Average()

sd= stdev()

The Z score values which are outside the range of -3 and 3 are considered as an outliers.

The Z score of X and Y does not contains any such values.

Therefore there is no outliers in the data.

From the two datat sets we find that the spread for the second data set is more than the first data set.

That mean the observations are more centered toward the mean.