Question

Waiting times​ (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two​ samples, then compare the two sets of results. Single Line 6.5 6.6 6.7 6.8 7.0 7.1 7.5 7.6 7.6 7.6 Individual Lines 4.2 5.4 5.8 6.2 6.5 7.6 7.6 8.6 9.2 9.9 The mean waiting time for customers in a single line is nothing minutes. The median waiting time for customers in a single line is nothing minutes. The mean waiting time for customers in individual lines is nothing minutes. The median waiting time for customers in individual lines is nothing minutes. Determine whether there is a difference between the two data sets that is not apparent from a comparison of the measures of center. If​ so, what is​ it? A. The times for customers in a single line are much more varied than the times for customers in individual lines. B. The times for customers in individual lines are much more varied than the times for customers in a single line. C. There is no difference between the two data sets.

Answer 1

Solution:

Single line:

Mean = (6.5 + 6.6 + 6.7 + 6.8 + 7.0 + 7.1 + 7.5 + 7.6 + 7.6 + 7.6)/10
= 71/10
Mean = 7.1

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

6.5   6.6   6.7   6.8   7.0   7.1   7.5   7.6   7.6   7.6   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = 7.0+ 7.1 /2 = 7.05

Individual Lines

Mean = (4.2 + 5.4 + 5.8 + 6.2 + 6.5 + 7.6 + 7.6 + 8.6 + 9.2 + 9.9)/10
= 71/10
Mean = 7.1

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

4.2   5.4   5.8   6.2   6.5   7.6   7.6   8.6   9.2   9.9   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = 6.5+ 7.6 /2 = 7.05

There is no difference between the two data sets.