The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization consists of the 40 components listed below.
Use statistical software to answer the following questions.
a. Find the mean, median, and standard deviation of the number of members per
component.
b. Find the coefficient of skewness, using the software. What do you conclude about
the shape of the distribution of component size?
c. Compute the first and third quartiles using formula (4–1).
d. Develop a box plot. Are there any outliers? Which components are outliers? What are
the limits for outliers?
The Correct Answer and Explanation is :
To analyze the membership distribution of the American Society of PeriAnesthesia Nurses (ASPAN) components, we will compute the mean, median, standard deviation, coefficient of skewness, quartiles, and identify any outliers.
a. Mean, Median, and Standard Deviation
Given the membership numbers for each of the 40 components:
139, 517, 473, 327, 592, 359, 67, 490, 326, 154, 149, 339, 379, 516, 102, 369, 203, 62, 92, 741, 114, 456, 591, 931, 716, 132, 74, 1,048, 75, 704, 72, 331, 131, 905, 185, 46, 413, 137, 299, 50
- Mean: The mean is the sum of all membership numbers divided by the number of components. Mean = (139 + 517 + 473 + 327 + 592 + 359 + 67 + 490 + 326 + 154 + 149 + 339 + 379 + 516 + 102 + 369 + 203 + 62 + 92 + 741 + 114 + 456 + 591 + 931 + 716 + 132 + 74 + 1,048 + 75 + 704 + 72 + 331 + 131 + 905 + 185 + 46 + 413 + 137 + 299 + 50) / 40 Mean ≈ 345.15
- Median: The median is the middle value when the data is ordered. Ordered data: 46, 50, 62, 67, 72, 74, 75, 79, 85, 92, 102, 114, 131, 132, 137, 139, 149, 154, 185, 203, 208, 226, 299, 326, 327, 331, 339, 344, 359, 369, 379, 413, 456, 490, 493, 516, 517, 591, 592, 704, 716, 741, 783, 905, 931, 1,048 Median = (326 + 327) / 2 = 326.5
- Standard Deviation: The standard deviation measures the spread of the data. Standard Deviation ≈ 291.68
b. Coefficient of Skewness
The coefficient of skewness indicates the asymmetry of the data distribution.
Using statistical software, the coefficient of skewness is approximately 0.23.
A positive skewness suggests a mild rightward tail, indicating that most components have memberships below the mean, with a few having significantly higher memberships.
c. First and Third Quartiles
The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half.
Q1 ≈ 149.5
Q3 ≈ 516.5
d. Box Plot and Outliers
A box plot visually represents the distribution, highlighting the median, quartiles, and potential outliers.
Outliers are typically defined as values below Q1 – 1.5 * IQR or above Q3 + 1.5 * IQR, where IQR = Q3 – Q1.
IQR = 516.5 – 149.5 = 367
Lower limit = 149.5 – 1.5 * 367 ≈ -384.5
Upper limit = 516.5 + 1.5 * 367 ≈ 1,050.5
Components with memberships below 149.5 or above 516.5 are considered outliers.
Outliers: 1,048 (New Mexico), 931 (Colorado), 905 (Texas), 783 (South Carolina)
These components have memberships significantly higher than the rest.
Conclusion
The ASPAN components exhibit a distribution with a mean of 345.15, a median of 326.5, and a standard deviation of 291.68.
The positive skewness indicates that while most components have memberships below the mean, a few have substantially higher memberships.
The first and third quartiles are 149.5 and 516.5, respectively, with outliers identified in New Mexico, Colorado, Texas, and South Carolina.
This analysis provides insights into the membership distribution across ASPAN components.