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 6.5 nbsp 6.7 nbsp 6.8 nbsp 7.2 nbsp 7.3 nbsp 7.4 nbsp 7.6 nbsp 7.7 nbsp 7.7

Bank B​ (individual lines): 4.3 nbsp 5.5 nbsp 5.8 nbsp 6.2 nbsp 6.8 nbsp 7.6 nbsp 7.8 nbsp 8.5 nbsp 9.4 nbsp 9.7 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 (CV) for the waiting times at Bank A (single line) is 6.7%, while for Bank B (individual lines), the CV is 24.5%.

Comparison:

The variation in waiting times is significantly higher at Bank B (individual lines) compared to Bank A (single line), indicating that the waiting times at Bank A are more consistent.

Would you like more details or have any questions?

Here are some related questions to further explore:

  1. How is the coefficient of variation different from standard deviation?
  2. Why is the coefficient of variation useful for comparing data sets?
  3. What would happen if we increased the sample size for each bank?
  4. How do outliers affect the coefficient of variation?
  5. Can you think of other real-life situations where the coefficient of variation could be applied?

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

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Math Problem Analysis

Mathematical Concepts

Statistics
Coefficient of Variation
Data Comparison

Formulas

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

Theorems

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Suitable Grade Level

Grades 10-12

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