A parking garage in Memphis monitors the time it takes customers to exit the parking structure from the time they get in their car until they are on the streets.

A sample of 28 exits was recently taken and is shown here.

Garage Exit (time in seconds)
83 138 145 147 130 79 156 156 90 85 68 93 178 76 73 119 92 146 88 103 116 134 162 71 181 110 105 74

a. Calculate the range, interquartile range, variance, and standard deviation for these sample data.

b. If the minimum time and the maximum time in the sample data are both increased by 10 seconds, would this affect the value for the interquartile range that you calculated in part a? Why or why not?

c. Suppose the clock that electronically recorded the times was not working properly when the sample was taken and each of the sampled times needs to be increased by 10 seconds. How would adding 10 seconds to each of the sampled speed of service times change the sample variance of the data?