Question

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. $$ \begin{array}{|lclc|} \hline \text { State/Region } & \text { Membership } & \text { State/Region } & \text { Membership } \\ \hline \text { Alabama } & 95 & \text { New Jersey, Bermuda } & 517 \\ \text { Arizona } & 399 & \text { Alaska, Idaho, Montana, } & \\ \text { Maryland, Delaware, DC } & 531 & \text { Oregon, Washington } & 708 \\ \text { Connecticut } & 239 & \text { New York } & 891 \\ \text { Florida } & 631 & \text { Ohio } & 708 \\ \text { Georgia } & 384 & \text { Oklahoma } & 171 \\ \text { Hawaii } & 73 & \text { Arkansas } & 68 \\ \text { Illinois } & 562 & \text { California } & 1,165 \\ \text { Indiana } & 270 & \text { New Mexico } & 79 \\ \text { lowa } & 117 & \text { Pennsylvania } & 575 \\ \text { Kentucky } & 197 & \text { Rhode Island } & 53 \\ \text { Louisiana } & 258 & \text { Colorado } & 409 \\ \text { Michigan } & 411 & \text { South Carolina } & 237 \\ \text { Massachusetts } & 480 & \text { Texas } & 1,026 \\ \text { Maine } & 97 & \text { Tennessee } & 167 \\ \text { Minnesota, Dakotas } & 289 & \text { Utah } & 67 \\ \text { Missouri, Kansas } & 282 & \text { Virginia } & 414 \\ \text { Mississippi } & 90 & \text { Vermont, } & \\ \text { Nebraska } & 115 & \text { New Hampshire } & 144 \\ \text { North Carolina } & 542 & \text { Wisconsin } & 311 \\ \text { Nevada } & 106 & \text { West Virginia } & 62 \\ \hline \end{array} $$ 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?

Name: Problem 28, Chapter 4: Basic Statistics for Business & Economics
Uploaded: 2022-01-18T23:49:12-08:00
Duration: 6 min 16 s
Channel: Jon Southam

   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.
$$
\begin{array}{|lclc|}
\hline \text { State/Region } & \text { Membership } & \text { State/Region } & \text { Membership } \\
\hline \text { Alabama } & 95 & \text { New Jersey, Bermuda } & 517 \\
\text { Arizona } & 399 & \text { Alaska, Idaho, Montana, } & \\
\text { Maryland, Delaware, DC } & 531 & \text { Oregon, Washington } & 708 \\
\text { Connecticut } & 239 & \text { New York } & 891 \\
\text { Florida } & 631 & \text { Ohio } & 708 \\
\text { Georgia } & 384 & \text { Oklahoma } & 171 \\
\text { Hawaii } & 73 & \text { Arkansas } & 68 \\
\text { Illinois } & 562 & \text { California } & 1,165 \\
\text { Indiana } & 270 & \text { New Mexico } & 79 \\
\text { lowa } & 117 & \text { Pennsylvania } & 575 \\
\text { Kentucky } & 197 & \text { Rhode Island } & 53 \\
\text { Louisiana } & 258 & \text { Colorado } & 409 \\
\text { Michigan } & 411 & \text { South Carolina } & 237 \\
\text { Massachusetts } & 480 & \text { Texas } & 1,026 \\
\text { Maine } & 97 & \text { Tennessee } & 167 \\
\text { Minnesota, Dakotas } & 289 & \text { Utah } & 67 \\
\text { Missouri, Kansas } & 282 & \text { Virginia } & 414 \\
\text { Mississippi } & 90 & \text { Vermont, } & \\
\text { Nebraska } & 115 & \text { New Hampshire } & 144 \\
\text { North Carolina } & 542 & \text { Wisconsin } & 311 \\
\text { Nevada } & 106 & \text { West Virginia } & 62 \\
\hline
\end{array}
$$
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?

Basic Statistics for Business & Economics

Douglas A. Lind,… 9th Edition

Chapter 4, Problem 28

Instant Answer

Solved by Expert Jon Southam

01/18/2022

Step 1

We can use the following formulas: - Mean: $\frac{\sum_{i=1}^{n} x_i}{n}$ - Median: Middle value of the sorted data - Standard Deviation: $\sqrt{\frac{\sum_{i=1}^{n} (x_i - \text{mean})^2}{n}}$ Show more…

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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. $$ \begin{array}{|lclc|} \hline \text { State/Region } & \text { Membership } & \text { State/Region } & \text { Membership } \\ \hline \text { Alabama } & 95 & \text { New Jersey, Bermuda } & 517 \\ \text { Arizona } & 399 & \text { Alaska, Idaho, Montana, } & \\ \text { Maryland, Delaware, DC } & 531 & \text { Oregon, Washington } & 708 \\ \text { Connecticut } & 239 & \text { New York } & 891 \\ \text { Florida } & 631 & \text { Ohio } & 708 \\ \text { Georgia } & 384 & \text { Oklahoma } & 171 \\ \text { Hawaii } & 73 & \text { Arkansas } & 68 \\ \text { Illinois } & 562 & \text { California } & 1,165 \\ \text { Indiana } & 270 & \text { New Mexico } & 79 \\ \text { lowa } & 117 & \text { Pennsylvania } & 575 \\ \text { Kentucky } & 197 & \text { Rhode Island } & 53 \\ \text { Louisiana } & 258 & \text { Colorado } & 409 \\ \text { Michigan } & 411 & \text { South Carolina } & 237 \\ \text { Massachusetts } & 480 & \text { Texas } & 1,026 \\ \text { Maine } & 97 & \text { Tennessee } & 167 \\ \text { Minnesota, Dakotas } & 289 & \text { Utah } & 67 \\ \text { Missouri, Kansas } & 282 & \text { Virginia } & 414 \\ \text { Mississippi } & 90 & \text { Vermont, } & \\ \text { Nebraska } & 115 & \text { New Hampshire } & 144 \\ \text { North Carolina } & 542 & \text { Wisconsin } & 311 \\ \text { Nevada } & 106 & \text { West Virginia } & 62 \\ \hline \end{array} $$ 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?

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Key Concepts

Quartiles

Quartiles are values that divide a data set into four equal parts, with each part representing one-quarter of the distributed sampled population. The first quartile (Q1) and the third quartile (Q3) are particularly important in assessing the spread and central tendency of the data. They are used to establish the interquartile range (IQR), which is a measure of statistical dispersion and is critical when identifying potential outliers in the data.

Box Plot and Outlier Detection

A box plot is a graphical tool used in exploratory data analysis that visually summarizes the distribution of a data set through its quartiles and highlights the central tendency and variability. It also identifies potential outliers by marking points that fall outside predetermined limits, commonly defined as 1.5 times the interquartile range (IQR) from the quartiles. This visualization aids in detecting abnormal observations and understanding the overall shape and spread of the data.

Descriptive Statistics

Descriptive statistics refer to summary measures that quantitatively describe the main features of a data set. In this case, it includes measures of central tendency, such as the mean and median, which give an indication of the typical value, as well as measures of dispersion, such as the standard deviation, which quantifies the amount of variation or spread in the data. These summaries provide a quick overview of the dataset’s characteristics and help in understanding its overall behavior.

Coefficient of Skewness

The coefficient of skewness is a numerical measure that quantifies the asymmetry of the distribution of data around its mean. A skewness value of zero indicates perfect symmetry, whereas a positive value indicates a long right tail and a negative value indicates a long left tail. In statistical analysis, skewness helps in assessing whether the data is normally distributed or if there are tendencies toward asymmetry that could affect further statistical inference.

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Transcript

00:01 All right, so we're using statistical software to answer the questions, and i'm using the spreadsheet to do that.

00:09 And what we're looking at is the american society of pari anesthesia nurses, and they had some data on their, the organization's 40 components and the membership within each of the components.

00:25 So it's the basically membership of their regional organizations.

00:30 And so there are 40 components as in states or certain regions like missouri and kansas are considered one, whereas indiana is its own and colorado is its own.

00:42 Whereas here, maryland, delaware, d .c.

00:46 Was one component.

00:51 And we're looking at how it's spread out, how the membership is spread out across these different regions.

00:59 So finding the mean, median, standard deviation.

01:02 So the mean, just use the average function, median, middle value.

01:12 And now i take the population standard deviation because this is the entire organization, all the components of the organization.

01:23 It's the entire population.

01:24 So i use the population to standard deviation.

01:31 So there's that.

01:41 And so that's what that means.

01:43 So that means within.

01:46 And since the mean and median are not, they're kind of spread out.

01:49 There's going to be some skewness here.

01:51 Segway into part b.

01:53 The coefficient of skewness using the software is the software formula.

02:00 And it's a positive number, which tells us that it is skewed in the positive direction or positively skewed, which we can see.

02:12 See that here the median is, the mean is bigger than the median.

02:15 And so it's skewing in the larger values.

02:19 And then part c to find the quartiles.

02:22 And so that's, these are the quartile values here.

02:25 This was the, the basically finding the percentile, the 25th and 75th percentile locations of them.

02:35 And then these are the formulas where you take that value plus that's the 10th value.

02:42 That's what the 10 means here.

02:44 The 10th was nevada 106.

02:47 Plus the difference between it and the next value, which is nine times the 0 .25.

02:53 And then the same thing for the third...

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