Question

1.  The following data show the number of days it took to close the sale of twenty homes for a particular lending institution.  Compute the mean, median, standard deviation and % coefficient of variation.  Are there any outliers (any values that exceed the mean by more than 3 standard deviations)?  If the expected value for the mean is 30 days, what is the percent bias and the sign?  (12 points)

       33                   35                  27                   31                  36

       32                   29                  35                   38                  32

       32                   34                  28                   31                  34

       36                   30                  32                   33                  34

Answer 1

The values in sorted order:

27 28 29 30 31 31 32 32 32 32 33 33 34 34 34 35 35 36 36 38

Mean = 32.6

Median = 32.5(average of 10th and 11th largest number) i.e average of 31 and 32

Standard deviation = 2.7985

Coefficient of variation = sd*110/mean = 2.7985*100/32.6 = 8.584%

mean + 3*sd = 40.9955 and mean - 3*sd = 24.2045. thus all the values beyond this are considered outliers. There are no outliers.

Percent bias = (expected-observed)*100/observed =(30-32.6)*100/32.6=-7.975