Math Problem Statement
A Providence Hospital experiment involves two different waiting line configurations for patients arriving for admission. The waiting times (in seconds) are recorded with a single line configuration that feeds four stations and another configuration with individual lines at the four stations. Find the coefficient of variation for each of the two samples, and then compare the variation.
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Part 1
Find the coefficient of variation of the single line data set.
enter your response here%
(Type an integer or a decimal rounded to one decimal place as needed.)
Part 2
Find the coefficient of variation of the individual lines data set.
enter your response here%
(Type an integer or a decimal rounded to one decimal place as needed.)
Part 3
Compare the variation. Choose the correct answer below.
A.
The variation of the single line is much larger than the variation of the individual lines because its CV is larger than the CV for the single line data set.
B.
The variation is roughly about the same because the two values of CV are approximately equal.
C.
The variation of the individual lines is much larger than the variation of the single line because its CV is larger than the CV for the single line data set.
D.
It is impossible to compare the variation with the information given.
Single Line
392
394
402
409
425
440
445
461
461
461
Individual Lines 254 322 350 370 401 462 462 510 559 601
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Coefficient of Variation
Standard Deviation
Mean
Formulas
Coefficient of Variation (CV) = (Standard Deviation / Mean) x 100%
Mean (μ) = Sum of values / Number of values
Standard Deviation (σ) = sqrt((1/(n-1)) * Σ(x_i - μ)^2)
Theorems
-
Suitable Grade Level
Grades 11-12
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