Exercise 1: Improving customer service A bank branch located in a commercial dis
ID: 2949202 • Letter: E
Question
Exercise 1: Improving customer service A bank branch located in a commercial district of a city has developed a process to improve customer service during the noon to 1 pm lunch period. The waiting time in minutes of all customers during this hour is recorded over a period of one week. The waiting time is defined as the time the customer enters the line to when he or she reaches the teller window. A random sample of 15 customers is selected, and the results are as follows: 4.21 5.55 0.55.13 4.77 2.34 3.54 3.2 4.5 6.1 0.38 5.12 6.46 12.19 3.79 Use an appropriate technique to summarise the data and answer following questions a) What are the shortest and the longest waiting times? b) What is the typical waiting time? c) Around what values, if any, are the waiting times concentrated?Explanation / Answer
a) The shortest waiting time is the minimum of all 15 observations = 0.38 min and the longest waiting time is the maximum of them = 12.19 min
b) The mean of this waiting times are (4.21+5.55 +0.5 + 5.13 + 4.77 + 2.34+ 3.54 + 3.2 + 4.5 + 6.1 + 0.38 + 5.12 + 6.46 + 12.19 + 3.79) / 15 = 67.78/15 = 4.52 min
Now, let's look at the data in the ascending order.
0.38 0.50 2.34 3.20 3.54 3.79 4.21 4.50 4.77 5.12 5.13 5.55 6.10 6.46 12.19
Now, notice that, while most of the value are within a band of 2.3 min to 6.5 min, there are three values which are kind of extreme in the sense that they are kind of outliers. So, in this situation, median might be a better measure of typical value than mean.
Median of the data = (15+1)/2 = 8th observation in the data sorted in ascending order above = 4.5 min, which comes similar to mean.
So, a typical value of waiting time is 4.5 min
c) The first quartile of the data is = Average of 4th and 5th observation in ascending order data =(3.20+3.54)/2 = 3.37 min and third quartile = Average of 11th and 12th observation in ascending order data = (5.13+5.55)/2 = 5.34 min
So, the waiting times are concentrated between (3.37, 5.54) min
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