# MATH 225N Discussion Measures of Central Tendency and Variation

## Sample Answer for MATH 225N Discussion Measures of Central Tendency and Variation Included After Question

**Initial Post Instructions**

For this Discussion, you will examine central tendency and variability in terms of pulse rate.

Find and record the pulse rate of 10 different people where you work. Tell us a little about the population from which you drew your data. Describe your findings in terms of central tendency and variability.

Consider using some of the following to help you form your initial discussion post:

What are your measures of central tendency (i.e., mean, median, and mode)? Which might be the better measure for central tendency and why?

What is the standard deviation of your data? How variable are the data (range)?

Are there any outliers? Investigate possible reasons for these outliers, and things that might limit them if further study were to be carried out.

What are some variables that should be considered in discussing your measures of central tendency and variation? Is there any skewness in your measured data?

How would you describe this data (i.e. what insights did you gain from this data)?

## A Sample Answer For the Assignment: MATH 225N Discussion Measures of Central Tendency and Variation

## Title: MATH 225N Discussion Measures of Central Tendency and Variation

I want to please make a couple of things clear here for uniformity and clarity and consistency.

**Please record the pulse rate for one minute / 60 seconds per person**.

If it is typical that you just “take” the pulse for 15 seconds and then therefore multiply it by 4 then so be it – you all would know much much better than me how things are done…

**But PLEASE everyone use a rate for a 60 seconds / one minute time period** so that we all can look at each other’s numbers ( data values ) and means and medians and sample standard deviations and so forth and all be on the same page and in the same frame of mind and have the same reference points and point of view and thinking and all that when looking at each other’s numbers and results.

**ALSO I want to make it clear that I am going to make a few Posts with an “Example” of these Week 3 questions and concerns but that my “example” will involve a sample size of n = 30**

## ALSO READ:

**MATH 225N Discussion The Normal Distribution**

**MATH 225N Discussion Confidence Intervals **

**MATH 225N Discussion Hypothesis Testing**

**MATH 225N Discussion Final Review**

**MATH 225N Discussion Correlation and Regression **

**MATH 225N Discussion Basic Statistics Data Used in Everyday Life **

**But you all please stick to the assignment instructions / directions and use a sample size of n = 10 please.**

Thanks and Best Wishes ! Have fun with this assignment !! **Use your Week 3 spread sheet( s ) on this assignment as much as you possibly can ! Even attach copies of your Week 3 spread sheet( s ) to your Posts with your actual 10 pieces of data filled in and so forth** ! Enjoy and Learn Friends !!!

Don’t forget the **lab turn in assignment in Week 3** !!!!

We have **Knewton Quizzes in Weeks 2 4 6 and lab turn in assignments in Weeks 3 5 7** .

It looks like you might have had some trouble trying to get a graphic / image into your Post and so I wanted to try it out for myself and see if I could get it to work. 😉

The process involved a couple of unexpected steps for me, so I will share as much as I can here to hopefully help Folks who might want to place something like this in a Post during Weeks X-X . 😉

XXXXX gave some great instructions on doing this kind of thing too, but I have a variation on a few of the steps that she performed. 😉

**Click here to ORDER an A++ paper from our Verified MASTERS and DOCTORATE WRITERS MATH 225N Discussion Measures of Central Tendency and Variation :**

First, before copying and pasting the Excel output to an open blank Word document, I had to go through the very irritating step of giving all the cells to be copied and pasted a sort of light background – that orangy peachy color that you see.

Otherwise when I created my jpg / jpeg most of the cells were dark black and not readable so to speak.

Next in Excel I highlighted the cells to be copied and then did contol c

Then in a blank Word document I used the mouse and clicked but had to be careful about which Paste option that I used – I had to use Paste as a picture, which was one of the last options available to me from left to right.

Then I clicked on the image in the Word document and did Save as Picture

Then I saved it to my desktop and saved it as a jpg / jpeg

Then in the course shell I clicked on Files and then clicked on Week X Files

Then I uploaded my newly created image from my desk top into the Week X Files area

Then in my Post I clicked on Embed Image and then clicked CANVAS and then clicked Course Files and then clicked Week X Files

Then I located my desired image and clicked on it

Then I scrolled down a bit and clicked Update or whatever it is…

Then the image magically appeared in this Post ! 🙂

So the two steps that surprised me the most were having to give all the cells a light background and secondly instead of just blindly pasting into Word I had to be thoughtful and intentional about “which” “paste method / type” to use.

Thanks XXXXX and Best Wishes and please enjoy the upcoming Week X and work hard and learn a lot !

I really appreciate that very much !!

And here is just an example Post showing you the potential to get Excel output into a graded Post and what it might look like and how it might work.

I will be making a lot of Posts throughout Week 3 showing and demonstrating for you how to do this. But you don’t have to wait for those Posts though if you don’t want to. There is already an 11 minute Video in Media Gallery along the left of the screen which shows you how to do this.

Thanks Friends and Best Wishes and Good Luck too !!

🙂

**PS** Even though it is a little fuzzy and blurry in the graphic / image here, that z-score is negative.

It is – 0.8 since 72 – 80 is of course negative. And then – 8 / 10 of course is – 0.8

**Required Resources**

Read/review the following resources for this activity:

- OpenStax Textbook: Chapter 2
- Lesson

- Chamberlain University Library

- Internet

**Scenario/Summary**

This week’s lab highlights the use of graphics, distributions, and tables to summarize and interpret data.

Follow the directions below to find one of the given academic articles from the Chamberlain library and then use that to describe the graphs and tables included. Further, you will describe other ways that the same data could be presented.

**Deliverables**

The deliverable is a Word document with your answers to the questions posed below based on the article you find.

**Required Software**

- Microsoft Word
- Internet access to read articles

**Steps to Complete Week 3 Lab**

**PART 1:**

Step 1: For our **first **broad-based search, choose ** one** of the articles listed below that interests you. Use the underlined words in your chosen article to search and see how many articles from the Pro-Quest Nursing database contain these underlined words (see the example below the article list)

**Article Titles (choose one!)**

- Oral manifestations in diabetic patients under treatment for ischemic heart diseases: A comparative observational study
- Systolic blood pressure , diastolic blood pressure, and pulse pressure: An evaluation of their joint effect on mortalityThe Relationship Between Body Mass Index (BMI) and Menstrual Disorders at Different Ages of Menarche and Sex HormonesAdolescents’ first tobacco products: Associations with current multiple tobacco product useAssociation of lifestyle modification and pharmacological adherence on blood pressure control among patients with hypertension at Kenyatta National Hospital, Kenya: A cross-sectional studyDemographic, parental, and personal factors and youth athletes’ concussion -related knowledge and beliefs Nutrition-related information-seeking behaviors of women trying to conceive and pregnant women: evidence for the life course perspective.Efficiency and optimal size of hospitals: Results of a systematic searchLong working hours, sleep-related problems, and near-misses/injuries in industrial settings using a nationally representative sample of workers in JapanDemographic Characteristics of RN and Generic Students: Implications for CurriculumClinical Characteristics of Diabetic Ketoacidosis in Children with Newly Diagnosed Type 1 Diabetes in Addis Ababa, Ethiopia: A Cross-Sectional Study

- Using Computerized Adaptive Testing to Reduce the Burden of Mental Health Assessment

Step 2: Go to the Chamberlain Library at https://library.chamberlain.edu (Links to an external site.)

Step 3: Click on the ProQuest Nursing link under the search box.

Step 4: Type the underlined words from the article that you chose into the first search bar. Checkmark **Full Text, Peer Reviewed, **and choose **Last 12 Months** from the drop down list. Last, choose **English Language** under the language section.

Step 5: Choose **Search** to see how many articles in the ProQuest database have those words.

Step 6: Post a screenshot of your search results (topic and the number of articles containing your search terms) to the top of a Word document [see Step 5 above]. Below the screenshot, answer the following questions:

On your search:

A. What terms did you use?

B. What other things did you mark on the search page before conducting your search?

C.Why did you choose the key words that you did?

D. How many articles were found with these search terms [from screenshot]?

**Part 2:**

Step 1: For our **second **more narrow search, go back and search using THE ENTIRE TITLE of the article you used the key words from in your first search. Paste the ENTIRE title into the search bar and find the full article [Do NOT checkmark anything to narrow your search this time!].

Step 2: Find a frequency table **and/or** graph within the article and post a screen shot in your Word document.

**Example:**

** Frequency Distribution **__OR__ Graph

__OR__Graph

Step 3: Answer the following questions about your table and/or graph:

A. What **type** of study is used in the article (quantitative or qualitative)?

B. What **type **of graph or table did you choose for your lab? What characteristics make it this type?

C.** Describe** the data displayed in your frequency distribution or graph (consider class size, class width, total frequency, list of frequencies, class consistency, etc)

D**. Draw a conclusion** about the data from the graph or frequency distribution you chose.

E. How else might this data have been displayed? Discuss pros and cons of **2 other presentation options**, such as tables or different graphical displays.

F. Give the full **APA reference** of the article you are using for this lab.

Step 5: Be sure your name is on the Word document, save it, and then submit it under “Assignments” and “Week 3: Lab”.

**Grading**

This activity will be graded based on the Week 3 Lab Rubric.

Edited by Christopher Smith on Jan 18, 2021 at 6:38am

Week 3 lab THIS is the TEMPLATE that you please use Math 225 Jan Feb 2021.docx

HERE ARE SOME MORE DETAILED HINTS 😉

**Body Mass Index article**: **focus on** Table 1 on page 441 left 2 columns

**Diabetes article**: **focus on** Table 6 on page 388

**Blood Pressure Control article**: **focus on** Figure 2 on page 4 ( the AGE part only with respective left to right counts of 92, 62, 75 which add up to the 229 )

**Blood pressure / mortality article**: **focus on** Table 2 on page 733 left 2 columns

Demographic characteristics students article: **focus on **Table 1 page 233

Income ( Monthly ) data

Long working hours Japan article: **focus on **Table 1 page 6 / 14

*EITHER* the Age data *OR* the Work hours per week data

Optimal size of hospitals article: **focus on **Table 1 page 9 / 40

focusing on the following information only:

class 1969 – 1989 with count 8

class 1990 – 2000 with count 25

class 2001 – 2014 with count 72

Women trying to conceive article: **focus on **Table 3 page i102

Diabetic ketoacidosis children article: **focus on **Table 1 page 5 / 9

Age category data

I don’t expect you all to do this unless you really wanted to ( Histogram pretty limited for just 10 pieces of data anyway ) but here is a Histogram for my 30 pieces of data:

And what we can see, and I am not too surprised, is that my data set of n = 30 resting heart rates is fairly bell shaped / symmetrical and is not really all that skewed left or skewed right.

This does not surprise me much at all.

Perfectly symmetrical / bell shaped would be like if there was all blue and no white under the red curve and no blue above or outside of the red curve so to speak.

But in my experience and to my way of thinking, these data do look fairly symmetrical / bell shaped.

OK so what I did now was to use the same 30 pieces of resting heart rate data and added two “made up” pieces of resting heart rate data ( 53 per minute and 126 per minute I think they were ) and when the program created the box and whiskers plot ( I also told the program to run diagnostics to look for potential outliers ) the program flagged both the 53 per minute and 126 per minute rates as being potential outliers ( indicated by the little blue dots ) .

You all actually had a few homework exercises along these lines where you found cutoffs for potential outliers using 1.5 times IQR and then seeing if any really low or really high pieces of data ( observations ) fell below the bottom cut off or above the top cut off. Remember that ?? It was probably a “select all that apply” type “multiple choice” exercise.

😉

🙂

Formula Card, Reference Sheet, and Standard Normal Distribution Table-2.pdf

Quartiles and Box Plots **( 57 minute mark to 1 hour, 19 minute mark )**

in the attached Video to see the stuff about using **fences** and the calculations involving **1.5 times IQR**

and all that stuff ( context is box and whisker plots ) for **trying to identify / flag outliers / potential outliers**.

The relevant formulas for the **fences** are on page one, right hand column of the attachment here. Any piece of original data that is below the lower **fence** or above the upper **fence** is **flagged as a potential outlier**.

As you have been finding out in your Weeks 1-3 Knewton Homework assignments, when there is a suspected outlier in the sample data, generally we shift towards preferring to use the median as a good measure of so-called central tendency.

On the other hand, if we don’t have any suspected outliers in the sample data, then we very often stick with preferring to use the mean as a good measure of central tendency.

When we say that we start to talk about and learn about distributions using shape, center, and spread, then what central tendency is – it is the fancy phrase or expression for “center.”

And the fancy phrase or expression for “spread” is “dispersion.”

Thanks Friends and I hope that you can conclude the Weeks 1-3 Knewton Homework assignments as quickly as possible and then try to dive into the Week 4 Knewton Homework assignments as quickly as is practical too !

Good Luck and Best Wishes Friends and THANK YOU for your hard work and attention !!

## SHAPES OF DISTRIBUTIONS

The most common shapes of distributions that we encounter and learn about in this course are symmetrical / bell shaped, skewed left, and skewed right. But there are many other shapes of distributions that you might come across in the online textbook readings such as uniform, bi modal, multi modal, and a few other possible shapes too. Thanks Friends and best wishes !! Remember that the direction of the skewness, if there is any noticeable or substantial skewness present at all, is “in the direction of the longer tail” so to speak. Good Luck Friends !! 🙂

Math 225 Statistics Week 3 slide deck-1.pdf

## Z-SCORES, UNUSUAL OBSERVATIONS, AND VERY UNUSUAL OBSERVATIONS

We explore potential / possible outliers in a data set using a concept involving the so-called fences in connection with a box and whiskers plot during Week 3. Concepts such as “unusual observations” and “very unusual observations” are separate from the concept of potential outlier and so I wanted to provide these slides here to try to reinforce what the situation and case is for how we identify and designate “unusual observations” and “very unusual observations” in a set of sample data. We will study and learn about z-scores in more detail during the upcoming Week 5 of the course. But we can please start to get acquainted with them here though. Thanks Friends and Enjoy Week 3 !! 🙂

Please ignore the written commentary at the bottom of this slide here. My reason for sharing this slide with you was just so that you could get a look at the graphic with the blue and pink and red areas / regions. Thanks Friends !! 🙂

## THE EMPIRICAL RULE

The Empirical Rule is also called the 68 95 99.7 Rule. You can sort of see why that would be the case by reviewing the slides below here.

One of the most important things to keep in mind about the Empirical Rule is that it DOES NOT apply to any data set in the universe – it only properly applies to certain data sets that satisfy certain conditions or criteria. But when the Empirical Rule does properly apply to a particular data set, then the information on the following slides can be used as a nice aid and tool while working out the solutions and answers to certain Empirical Rule “related” problems and exercises. Thanks Friends and Best Wishes !! 🙂

The way the answer was worked out for the example problem / exercise here was as follows:

We need the numerical labels for the seven “notches” or “tick marks” on the horizontal axis.

The middle of these seven notches or tick marks is x = 64.3 ( which is the mean here )

Then we do these calculations to find the other six numerical labels for the tick marks:

64.3 – 2.62 – 2.62 – 2.62 = 56.44

64.3 – 2.62 – 2.62 = 59.06

64.3 – 2.62 = 61.68

64.3 + 2.62 = 66.92

64.3 + 2.62 + 2.62 = 69.54

64.3 + 2.62 + 2.62 + 2.62 = 72.16

So that the labels ( and these are x values and NOT z values ) for the seven tick marks from left to right in the picture then are:

56.44 59.06 61.68 64.3 66.92 69.54 72.16

And so when answering the question having to do with the percent of women whose heights are between 59.06 inches and 64.3 inches, what we see from the picture in the last slide above is that 13.5% occurs between x = 59.06 and x = 61.68 and that another 34% occurs between x = 61.68 and x = 64.3, and so that therefore the total percentage occurring between x = 59.06 and x = 64.3 is 13.5% + 34% = 47.5%

** Please** remember that in these graded Posting Assignments as well as in the Lab turn in Assignments, there are some very important requirements and standards and best practices involving references and referencing and most notably with regard to potential plagiarism and requirements for so called

**in text citations**.

**PLEASE** **remember that directly quoted material MUST have quote marks !! No exceptions !!!**

There is a difference between content and info that is paraphrased and content and info that is directly quoted.

Also, many class members tend to struggle some with proper and full and appropriate **in text citations**, and some class members at times leave them out all together. This is absolutely not acceptable either.

For each reference / resource listed at the end, there MUST be one or more corresponding and accompanying **in text citations** in the body / text of the work in question – whether it is a graded discussion post or a lab turn in assignment.

** Please** see the attached file for some examples of

**in text citations**for some common scenarios and situations.

It is also available in **Week 3 Files** after first clicking **Files** along the left of the computer screen.

** Thanks very much** and

**Friends and**

*best wishes***too !!**

*Good Luck***Please** remember that if you ever want anyone to listen to anything that you have to say ( I am talking about things you “say” through written expression ) , then you MUST be extremely thorough and keen and complete and correct and conscientious about formatting and standards and best practices and most notably something along the lines of **APA formatting** or in other contexts / settings other **Style Manuals** or things similar to **Style Manuals**.

** Enjoy** and learn a lot and work hard too !

The HR rate date that I collected in my nursing job in the Adult Day Care Center correspond to a group of patients older that 70 and that have history of HTN, DM, CAD among other chronic diseases.

HR Data is as follow. I arranged it from lower to higher values:

66, 68, 68, 70, 72, 76, 78, 82, 84, 99

According to A measure of central tendency is an important aspect of quantitative data. It is an estimate of a “typical” value. Three of the many ways to measure central tendency are the **mean, median and mode**” (online.stat.psu.edu, n.d.)

The central tendency of my data is:

Mean; 76

Medium: 74.3. This value does not belong to my data. According to Holmes this number is the center value of the data and it divide the data to the half (Holmes & Illowsky, 2018)

Mode: 78

. Since according to itl.nist.gov “an outlier is an observation that lies an abnormal distance from other values in a random sample from a population” (itl.nist.gov, n.d.). In this data there are not any outlier because all the values of my data are pretty close one to each other.

## References

Holmes, A., & Illowsky, B. &. (2018). *Introductory Business Statistic.* Texas: OpenStax.

itl.nist.gov. (n.d.). *What are outliers in the data?* Retrieved from Engineeiring Stadistic Handbook: https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm

online.stat.psu.edu. (n.d.). *Measures of Central Tendency*. Retrieved from PennState Eberly College of Science: https://online.stat.psu.edu/stat500/lesson/1/1.5/1.5.1

## A Sample Answer 2 For the Assignment: MATH 225N Discussion Measures of Central Tendency and Variation

## Title: MATH 225N Discussion Measures of Central Tendency and Variation

My data set is as follows: 68,73,78,80,85,91,95,99,100,112

This data was collected on my unit at work. The population I collected from were all nurses that I work with ranging in age from 21-37 years-of-age. Fitness level and health also varied. Also, not everyone was doing the same thing, giving a perspective of active versus resting heart rate.

Mean: 88

Median: 88

Mode: N/A; no value appears more than once

Range: 44

Outliers: None. To figure out if there were any outliers in my data set, I utilized the interquartile range formula. This also results in a symmetrical graph of the data.

This data set is a sample of the people I work with, not a whole population. Therefore, the standard deviation is 13.6789.

Being that there were no outliers in my data set either the mean or median would work to measure central tendency of the data. If the data presented had an outlier the better suited measure of central tendency would be the median (Holmes, Illowsky, & Dean, 2017). With the lack of outliers, I chose to plot the data using a box and whisker plot. A box and whisker plot is a visually effective way to plot variations in data that shows all aspects of the data set (What is a Box and Whisker Plot, 2020).

Brennaa Sullivan

## References:

Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory Business Statistics. OpenStax.

What is a box and Whisker Plot? (2020). *American Society for Quality*. https://asq.org/quality-resources/box-whisker-plotLinks to an external site.