Question

The manager of the Clark Fork Station Restaurant recently selected a random sample of 18 customers and kept track of how long the customers were required to wait from the time they arrived at the restaurant until they were actually served dinner. His study resulted from several complaints the manager had received from customers saying that their wait time was unduly long and that it appeared that the objective was to keep people waiting in the lounge for as long as possible to increase lounge business. The following data were recorded, with time measured in minutes:

34   43 24   54   43   34   56   27   74   34   20   36   19   24   33   54   55   39

1. Compute the mean, median, range, variance, standard deviation, and mode(s).

Mean	Median	Range	Variance	Std Deviation	Mode(s)

1. Construct an appropriate chart to describe the shape of this data set. Justify your answer.

1. Is the point 74 an outlier? Justify your answer.

1. Which measure of location provides the best measure of the center of this data? Justify your answer.

1. Why should the manager be concerned about the measures of variation? Explain briefly in words (within the context of this problem).

1. Which measure of variation provides the best measure of this data? Justify your answer.

Answer 1

a)

Mean	39.1
Median	35
Range	55
Variance	219.2
S.D	14.8
Mode	34

b)

It is a scatterplot.

c)

If X = 79

z = (79 - 39.1) / 14.8 = 39.9/14.8 = 2.70

Any z-score greater than 3 or less than -3 is considered to be an outlier.

Hence, this is not an outlier.

d)

There are not many outliers here. Hence, mean shows the center in an effective way here.