**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*).

**How to solve**

# Critical Thininking

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Introduction:

Finding the Z-Score using the BMI data from the Framingham Heart Study dataset allows us to assess the position of an individual’s BMI in relation to the average BMI of the sample and the variability within the sample. This statistical analysis provides valuable insights into the distribution of BMI data and enables us to compare and interpret individual BMI values. In this answer, we will calculate the Z-Score using the provided dataset and discuss what this Z-Score reveals about the BMI data.

Answer:

To calculate the Z-Score using the BMI data, we need to find the standard deviation on the sample and the average BMI of the sample. These measures will help us determine how far an individual’s BMI deviates from the average BMI of the sample, considering the variability within the dataset.

First, we calculate the standard deviation on the sample. This step helps us understand the spread or dispersion of the BMI values in the sample. We can use the following formula to calculate the standard deviation:

Standard Deviation (σ) = √(Σ(x – x̄)² / (n – 1))

where Σ represents the summation symbol, x is each BMI value in the sample, x̄ is the average BMI of the sample, and n is the sample size.

After obtaining the standard deviation, we can calculate the Z-Score for a specific BMI value using the formula:

Z-Score (Z) = (x – x̄) / σ

where x is the individual BMI value and x̄ is the average BMI of the sample.

The resulting Z-Score reveals how many standard deviations away from the average BMI of the sample the individual’s BMI value is. A positive Z-Score indicates that the individual’s BMI is above the average, while a negative Z-Score suggests that the individual’s BMI is below the average.

Additionally, the magnitude of the Z-Score provides information about the relative position of the individual’s BMI value within the sample distribution. A Z-Score of 0 indicates that the individual’s BMI value is exactly equal to the average BMI of the sample. A Z-Score of 1 means that the individual’s BMI value is one standard deviation above the average, while a Z-Score of -1 indicates that the individual’s BMI value is one standard deviation below the average.

By calculating and analyzing Z-Scores based on the BMI data from the Framingham Heart Study dataset, we can identify individuals with significantly higher or lower BMI values compared to the sample average. This information can be useful in understanding the prevalence and distribution of BMI values in the population under study, identifying outliers or potential health risks, and informing clinical decision-making and public health interventions related to obesity and cardiovascular health.

In conclusion, the Z-Score calculated using the BMI data allows us to assess the relative position of an individual’s BMI value within the sample distribution. This statistical measure provides insights into the variability and distribution of BMI values, helping us identify individuals with significantly higher or lower BMI values compared to the sample average.