In the last five years, many retailers have installed self-checkout stations for
ID: 3200813 • Letter: I
Question
In the last five years, many retailers have installed self-checkout stations for customers. The table below shows self-checkout times, in seconds, for a random sample of 25 shoppers at the University Village QFC [Quality Food Centers] grocery store: The [sample] mean equals 126.8 seconds and the [sample] standard deviation equals 99.748 seconds. Interpret (briefly) the value for the standard deviation. What percent of self-checkout times in the sample are within (plusminus) two standard deviations of the mean? Construct the associated five-number summary to represent all 25 self-checkout times. Which, if any, of the 25 self-checkout times are outlying/extreme values?Explanation / Answer
(a) Standard deviation is 99.748 seconds means, on an average, the self-checkout times vary from the mean value by about 99.748 seconds
(b) The limits are 126.8 ± 2(99.748) = [-72.696, 326.296]
The checkout times in the ascending order are
29, 33, 45, 47, 55, 64, 67, 71, 76, 82, 92, 96, 97, 105, 111, 123, 135, 141, 149, 156, 163, 184, 249, 320, 480
24 data lie in the above interval. Percentage = (24/25) * 100 = 96%
(c) Q2 = 97, Q1 = (64 + 67)/2 = 65.5, Q3 = (149 + 156)/2 = 152.5, Minimum = 29, Maximum = 480
The 5-number summary is {29, 65.5, 97, 152.5, 480}
(d) 320 is an outlier and 480 is an extreme value.
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