examining central tendency and variability based on two separate variables
Week 3 Discussion
Below I have listed the pulse rates of 10 different people from my office. There are 10 women in the office where I work, most of which are in the age range of 50 to 60’s and are all nurses. To maintain confidentiality, I used the age they reported to me with their pulse.
Ages: 54 51 55 56 64 57 60 55 60 58
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Pulses: 82 64 68 86 70 68 80 76 70 68
Our readings this week describe the central tendency to be the “average” or the “center of our data values” (Holmes, et al. 2017). If I was to describe my results based on central tendency and variability I would say that the total of all the pulses together equal 732, divide the 732 by 10 total people equals 73.2 which is the “mean” or the “arithmetic mean” or “average” (Holmes, et al. 2017). The mean and the median are the measures most used to determine the center of a set of valued (Holmes, et al. 2017). The median is the number in the “center” of the values and in this case, it is located between the 70th value and the 2nd 70th value, adding the two values together, 70+70 = 140 divide by 2 = 70 so the median is 70. Half of the values (pulses) are lower than 70 and half of the values (pulses) are higher than 70. The most frequent value or the mode is 68. The range is the 22 (max-min=range or 86-64=22).
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The numbers from lowest to highest: 64 68 68 68 70 70 76 80 82 86
64(1) + 68(3) + 70(2) + 76(1) + 80(1) + 82(1) + 86(1)
The better measure for central tendency I would say is the median which appears to be the center or exact middle of the values. It is the measure most used and to obtain the median, you add all the values and divide by the number of values. The median separates the values right up the middle so that both sides are equal (Holmes, et al. 2017).
Q3(80) – Q1(68) = IQR (12)
(1.5)(IQR)= 1.5×12=18 below the 1st Quartile 68 – 18 = 50
(1.5)(IQR)=1.5×12=18 above the 3rd Quartile 80 + 18 = 98
There are no outliers, not one person had a pulse 18 greater than the 3rd quartile or 98 and not one person had a pulse 18 lower than the 1st quartile or 50. However, if we included more than 10 people in this study, we could have had people with a pulse that was 18 points higher than the 3rd quartile such as 98 or 102 which would be considered outliers in this sample. There is a low standard deviation because the values are close to the mean, there is a smaller range.
Skewedness leaned toward the right as the pulses increased, the frequency remained at one with each of the greater pulses. Variables that need to be discussed when measuring central tendency and variation should include the size of the population and the possible ranges of the data. This data obtained from the population appeared to remain close to the mean when I wrote this information out and on a graph. The frequency of 1 occurred most often with the pulses. It seems the bigger a population the more information which may provide a much bigger range and you could possibly have some outliers. The data that I obtained may be biased as they are all women and nurses. There is a chance they have all taken medications to control their blood pressure and pulse and thereby all falling within the range of 64 to 86 pulse rates.
This week I read an article about the Joint Commission requiring hospitals to develop fall prevention programs for hospitalized children and monitor whether or not these programs are effective in decreasing rates of falls in hospitals. (Murray, E. 2016). Hospitalized children are at greater risk of falls due to their stages of development, age of the child, cognitive effects, medications and/or treatments, and equipment (Murray. E. 2016). These falls increase complications for patients and their length of stay in hospitals. Educating staff and using tools to assess patients risk of a fall increases the staff’s awareness to monitor those at risk more to decrease the incidents. The results indicated that there was a decreased rate of falls with pediatrics however, the study was with a limited population, not the entire hospital and earlier in the article it was mentioned that falls with no visible injuries are less likely to be reported so the study can really be biased. This made me think of how easily a study like this could easily be skewed and how the information obtained may not be reliable.
References:
Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory business statistics. OpenStax. (Section 2.1). Retrieved from: https://openstax.org/details/books/introductory-business-statistics (Links to an external site.)Links to an external site..
Murray, E. (2016). Quality Improvement. Implementing a Pediatric Fall Prevention Policy and Program. Pediatric Nursing, 42(5), 256-259. Retrieved from: https://chamberlainuniversity.idm.oclc.org/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=c8h&AN=118640418&site=ehost-live&scope=site
Central Tendency and Variability: Understanding descriptive statistics and their variability is a fundamental aspect of statistical analysis. On their own, descriptive statistics tell us how frequently an observation occurs, what is considered “average”, and how far data in our sample deviate from being “average.” With descriptive statistics, we are able to provide a summary of characteristics from both large and small datasets. In addition to the valuable information they provide on their own, measures of central tendency and variability become important components in many of the statistical tests that we will cover. Therefore, we can think about central tendency and variability as the cornerstone to the quantitative structure we are building.
For this Discussion, you will examine central tendency and variability based on two separate variables. You will also explore the implications for positive social change based on the results of the data.
To prepare for this Discussion:
Review this week’s Learning Resources and the Descriptive Statistics media program.
For additional support, review the Skill Builder: Visual Displays for Categorical Variables and the Skill Builder: Visual Displays for Continuous Variables, which you can find by navigating back to your Blackboard Course Home Page. From there, locate the Skill Builder link in the left navigation pane.
Review the Chapter 4 of the Wagner text and the examples in the SPSS software related to central tendency and variability.
From the General Social Survey dataset found in this week’s Learning Resources, use the SPSS software and choose one continuous and one categorical variable Note: this dataset will be different from your Assignment dataset).
As you review, consider the implications for positive social change based on the results of your data.
By Day 3 of central tendency and variability
Post, present, and report a descriptive analysis for your variables, specifically noting the following:
For your continuous variable:
Report the mean, median, and mode.
What might be the better measure for central tendency? (i.e., mean, median, or mode) and why?
Report the standard deviation.
How variable are the data?
How would you describe this data?
What sort of research question would this variable help answer that might inform social change?
Post the following information for your categorical variable:
A frequency distribution.
An appropriate measure of variation.
How variable are the data?
How would you describe this data?
What sort of research question would this variable help answer that might inform social change?
Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.
By Day 5 of central tendency and variability
Respond to at least one colleagues’ post with a comment on the presentation and interpretation of their analysis. In your response, address the following questions:
Was the presentation of results clear? If so, provide some specific comments on why. If not, provide constructive suggestions.
Are you able to understand how the results might relate back to positive social change? Do you think there are other aspects of positive social change related to the results?
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