Math Problem Statement

Waiting times​ (in minutes) of customers at 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 coefficient of variation for each of the two sets of​ data, then compare the variation. Bank A​ (single line): 6.5 nbsp 6.6 nbsp 6.7 nbsp 6.9 nbsp 7.2 nbsp 7.3 nbsp 7.5 nbsp 7.7 nbsp 7.7 nbsp 7.7

Bank B​ (individual lines): 4.3 nbsp 5.4 nbsp 5.7 nbsp 6.2 nbsp 6.8 nbsp 7.6 nbsp 7.8 nbsp 8.6 nbsp 9.3 nbsp 9.9 Question content area bottom Part 1 The coefficient of variation for the waiting times at Bank A is    enter your response here​%. ​(Round to one decimal place as​ needed.)

Solution

The coefficient of variation for the waiting times at Bank A is approximately 6.6%, and for Bank B, it is approximately 25.2%.

Comparing the two, Bank B (with individual lines) has much higher variability in waiting times compared to Bank A (with a single line), indicating that wait times are more inconsistent in Bank B.

Would you like further details on the calculation or the comparison? Here are some related questions to consider:

  1. What is the significance of the coefficient of variation in comparing data sets?
  2. How does the standard deviation affect the coefficient of variation?
  3. How might this variability affect customer satisfaction in each bank?
  4. Can we use the same analysis for other service systems, such as restaurants?
  5. How does the mean waiting time differ between Bank A and Bank B?

Tip: The coefficient of variation is particularly useful when comparing the relative variability between data sets with different means.

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Math Problem Analysis

Mathematical Concepts

Statistics
Coefficient of Variation
Standard Deviation
Mean

Formulas

Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100

Theorems

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Suitable Grade Level

Grades 9-12

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