**Measures of Central Tendency and Variation**

Understanding descriptive statistics, their measures of center and their variability, helps form the foundation of statistical analysis. 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 these statistics, we are able to provide a summary of characteristics from both large and small datasets. Measures of central tendency and variability provide valuable information on their own, and form the cornerstone of the quantitative structures that we build in our research studies.

Required Resources

Read/review the following resources for this activity:

OpenStax Textbook: Chapter 2

Lesson

Minimum of 1 scholarly source

In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).

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)?

**Sample Paper**

**Measures of Central Tendency and Variation**

The resting pulse rates for ten people were 64, 72, 88, 73, 55, 84, 90, 73, 76, and 74. The sample represents a culturally diverse group of young and middle-aged adults. Five of the subjects were men, and the other half were women. The most significant variation was their lifestyles, as some were more physically active than others.

The mean pulse rate is (64 +72+ 88 + 73 + 55 + 84 + 90 + 73 + 76 + 74)/10 = ** 74.9** The mode is

**, since it appears more than any other value (twice). Next, one can compute the median as follows:**

__73__(55, 64, 72, 73, 73, 74, 76, 84, 88, 90). The two central numbers are 73 and 74. Hence, the median is (73+74)/2 = ** 73.5**. Finally, the data set’s standard deviation is

**10.61917**(see figure 1), and the data’s range is

__55-90.__The data set contains two outliers, one of each end. They could have occurred due to the subject’s fitness levels. Highly athletic individuals tend to have a lower pulse rate due to physical conditioning (Bell, 2020). Conversely, people who rarely get enough exercise and are obese fall on the other side of the pulse rate spectrum (Yadav et al., 2017). Therefore, the contrasting diversity in physical wellness could explain the outliers. Conducting a more comprehensive study may limit these outliers if one chooses to group the data according to lifestyles, such as activity level and diet. Hence, each data set would contain relatable values.

Whenever one discusses measures of central tendency and variation, one must consider some confounding factors. These vary depending on the phenomenon under investigation (Holmes et al., 2017), but if it is related to human health, elements such as age, gender, and genetics are significant.

The dataset has a skewness of -0.3211 (see figure 1). Thus, there are more values below the median but have less weight than those above it. The data shows that even a medical value such as pulse rate can have essential variations. One should consider crucial physical and social parameters before deciding what the pulse rate means for that person’s overall well-being.

Figure 1: Excel computation of skewness and other measures

**References**

Bell, M. A. (2020, Apr. 21). Why Do Athletes Have a Lower Resting Heart Rate? https://www.healthline.com/health/athlete-heart-rate#ideal-resting-rate

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

Yadav, R. L., Yadav, P. K., Yadav, L. K., Agrawal, K., Sah, S. K., & Islam, M. N. (2017). Association between obesity and heart rate variability indices: an intuition toward cardiac autonomic alteration – a risk of CVD. *Diabetes, metabolic syndrome, and obesity: targets and therapy, 10*, 57–64. https://doi.org/10.2147/DMSO.S123935