Question

A very busy and fancy restaurant records the wait time for each customer that comes in. Below are 12 customers’ wait times (in minutes):

51        60        59        72        80        83        54        66        61        81        66        62

(a) What is the mean wait time?

(b) What is the median wait time?

(c) What is the variance in wait times?

(d) What is the unbiased standard deviation in wait times? Why would the standard deviation be more informative of a statistic than the variance?

(e) What is the first quartile? Third quartile?

(g) List the 5 number summary of the data.

Answer 1

Following table shows the calculations:

	X	(X-mean)^2
	51	232.5625
	60	39.0625
	59	52.5625
	72	33.0625
	80	189.0625
	83	280.5625
	54	150.0625
	66	0.0625
	61	27.5625
	81	217.5625
	66	0.0625
	62	18.0625
Total	795	1240.25

(a)

(b)

Following is the ordered data set:

S.No.	X
1	51
2	54
3	59
4	60
5	61
6	62
7	66
8	66
9	72
10	80
11	81
12	83

Since there are 12 data values so median will be average of 6th and 7th data values. That is median is

(c)

(d)

(e)

There are 6 data values in first half of data set so first quartile will be average of 3rd and 4th data values. So

There are 6 data values in second half of data set so third quartile will be average of 9th and 10th data values. So

(g)

Five number summary:

Min = 51

First quartile = 59.5

Median = 64

Third quartile = 76

Max. = 83