Question

1. The following set of data is from a sample of n = 7: 3 14 11 6 2 14 13

A. Compute the range, variance, standard deviation, and coefficient of variation.

B. Compute the Z score for each observation. Assuming a Z-score of 2 or greater represents an outlier, are there any outliers in this data set?

Answer 1

A)  

Range = Maximum value - Minimum value.

= 14 - 2

Range = 12

Mean $\bar{x}$ = $\sum$ X / n = 63/7 = 9

Variance = $\sum$ X² - n$\bar{x}$² / n-1

= 731 - 7 * 9² / 6

Variance = 27.3333

Standard deviation = Sqrt(Variance)

= sqrt( 27.3333)

Standard deviation = 5.2281

Coefficient of variation = Standard deviation / mean *100

= 5.2281 / 9 * 100

Coefficient of variation = 58.09%

B)

Z-Score = (X - Mean) / Standard deviation , Where X is score.

For X = 3

z = 3 - 9 / 5.2281

= -1.15

For X = 14

z = 14 - 9 / 5.2281

= 0.96

For X = 11

z = 11 - 9 / 5.2281

= 0.38

For X = 6

z = 6 - 9 / 5.2281

= 0.57

For X = 2

z = 2 - 9 / 5.2281

= 1.34

For X = 14

z = 14 - 9 / 5.2281

= 0.96

For X = 13

z = 13 - 9 / 5.2281

= 0.77

Since all z score are between -2 and 2 , there are no outliers.