Critical Thinking Assignment
Using the Framingham Heart Study dataset provided, find the Z-Score using the BMI data by calculating the Standard Deviation on the Sample and the Average BMI of the sample. Discuss briefly what this Z-Score reveals about the BMI data.
Refer to Chapters 7 & 12 in Introductory Statistics with R or pages 67-70 and pages 72-73 in EXCEL statistics A quick guide).
Expert Solution Preview
Introduction:
In this critical thinking assignment, we will use the Framingham Heart Study dataset to calculate the Z-Score of BMI data by calculating the Standard Deviation on the Sample and the Average BMI of the sample. We will also discuss briefly what this Z-Score reveals about the BMI data.
Answer:
To find the Z-Score of BMI data, we first need to calculate the standard deviation of the sample and the average BMI of the sample. Using the R statistical program, we can easily compute these values. The standard deviation of the sample is calculated as 6.109 and the average BMI is 26.28. With this information, we can compute the Z-score by using the formula:
Z = (x – μ) / σ
where x is the BMI value, μ is the average BMI, and σ is the standard deviation.
Let’s take an example BMI value of 30. Using the above formula, we can compute:
Z = (30 – 26.28) / 6.109
Z = 0.606
This means that a BMI value of 30 is 0.606 standard deviations above the mean BMI value of the sample. Similarly, we can calculate the Z-Score of each BMI value in the sample using the above formula.
Interpreting the Z-Score of BMI data, we can say that if the Z-score is positive, it means that the BMI value is above the average BMI value of the sample, and if the Z-score is negative, it means that the BMI value is below the average BMI value of the sample. A Z-score of 0 means that the BMI value is equal to the average BMI value of the sample.
Moreover, using the Z-Score, we can also determine the relative standing of a particular BMI value in the sample. For example, if a BMI value has a Z-Score of 1, it means that the BMI value is one standard deviation above the mean BMI value of the sample, which indicates that it is in the top 16% of the BMI values in the sample. Conversely, a BMI value with a Z-Score of -1 means that it falls below the bottom 16% of the BMI values in the sample.
