Questions: A Providence Hospital experiment involves two different waiting line configuration that feeds four stations and another configuration with individ compare the variation. Find the coefficient of variation of the single line data set. Single Line: 389, 398, 403, 410, 424, 439, 446, 463, 463, 463 Individual Lines: 250, 323, 348, 371, 404, 464, 464, 510, 560, 600 % (Type an integer or a decimal rounded to one decimal place as needed.)

A Providence Hospital experiment involves two different waiting line configuration that feeds four stations and another configuration with individ compare the variation.

Find the coefficient of variation of the single line data set.

Single Line: 389, 398, 403, 410, 424, 439, 446, 463, 463, 463

Individual Lines: 250, 323, 348, 371, 404, 464, 464, 510, 560, 600

%
(Type an integer or a decimal rounded to one decimal place as needed.)

Transcript text: A Providence Hospital experiment involves two different waiting line configuration that feeds four stations and another configuration with individ compare the variation. Find the coefficient of variation of the single line data set. \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Single Line & 389 & 398 & 403 & 410 & 424 & 439 & 446 & 463 & 463 & 463 \\ \hline Individual Lines & 250 & 323 & 348 & 371 & 404 & 464 & 464 & 510 & 560 & 600 \\ \hline \end{tabular} $\square$ \% (Type an integer or a decimal rounded to one decimal place as needed.)

Solution

Solution Steps

Step 1: Calculate the Sample Mean

For the first dataset, the sample mean ($\bar{x}_1$) is calculated as $\bar{x}_1 = \frac{\sum x_{i}}{n_1} = 429.8$. For the second dataset, the sample mean ($\bar{x}_2$) is calculated as $\bar{x}_2 = \frac{\sum x_{2i}}{n_2} = 429.4$.

Step 2: Calculate the Sample Standard Deviation

For the first dataset, the sample standard deviation ($s_1$) is $s_1 = \sqrt{\frac{\sum(x_{i} - \bar{x}_1)^2}{n_1-1}} = 28.8$. For the second dataset, the sample standard deviation ($s_2$) is $s_2 = \sqrt{\frac{\sum(x_{2i} - \bar{x}_2)^2}{n_2-1}} = 110.2$.

Step 3: Calculate the Coefficient of Variation

The coefficient of variation for the first dataset (CV1) is $CV1 = \frac{s_1}{\bar{x}_1} \cdot 100\% = 6.7\%$. The coefficient of variation for the second dataset (CV2) is $CV2 = \frac{s_2}{\bar{x}_2} \cdot 100\% = 25.7\%$.

Step 4: Compare the Coefficients of Variation

The coefficient of variation for the first dataset is less than that of the second dataset, indicating that the first dataset has less variability relative to its mean compared to the second dataset.