Question

9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the sample data below, find the following for each sample:

1. Range
2. Standard deviation
3. Variance

Lastly, compare the two sets of results.

Company	Wait times in seconds
Big Burger Company	105	67	78	120	175	115	120	59
The Cheesy Burger	133	124	200	79	101	147	118	125

Answer 1

Let x be wait times in seconds for Big Burger Company

and y be wait times in seconds for the Cheesy Burger company.

n = 8

x			y
105	0.125	0.015625	133	4.625	21.39063
67	-37.875	1434.516	124	-4.375	19.14063
78	-26.875	722.2656	200	71.625	5130.141
120	15.125	228.7656	79	-49.375	2437.891
175	70.125	4917.516	101	-27.375	749.3906
115	10.125	102.5156	147	18.625	346.8906
120	15.125	228.7656	118	-10.375	107.6406
59	-45.875	2104.516	125	-3.375	11.39063

For Big Burger company,

Range = Largest observation - smallest observation

           = 175 - 59

           = 116

Range = 116

Variance:

             (Round to 4 decimal)

Variance = 1391.2679

Standard deviation

s = 37.2997       (Round to 4 decimal)

Standard deviation = 37.2997

For the Cheesy Burger company,

Range = Largest observation - smallest observation

           = 200 - 79

          = 121

Range = 121

Variance:

           (Round to 4 decimal)

Variance = 1260.5536

Standard deviation:

s = 35.5043          (Round to 4 decimal)

Standard deviation = 35.5043

Here Variance of Big Burger company is greater than variance of Cheesy Burger company.

That means the data set Big Burger company has more spread than Cheesy Burger company.