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.
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Introduction:
The Z-Score is a commonly used statistical measurement that helps to understand how an individual measurement compares to the average measurement of a group. In the context of BMI data, calculating the Z-Score can provide insights into how a person’s BMI compares to the average BMI of a given sample population. By calculating the Standard Deviation and Average BMI of the sample, we can determine the Z-Score and analyze what it reveals about the BMI data.
Answer:
To find the Z-Score, we first need to calculate the Standard Deviation of the BMI data on the sample and the Average BMI of the sample population. The Standard Deviation measures the dispersion of the BMI values, while the Average BMI provides the central tendency of the data.
Once we have these values, we can calculate the Z-Score using the formula:
Z-Score = (Individual BMI – Average BMI) / Standard Deviation
The Z-Score is essentially the number of standard deviations an individual BMI measurement is away from the average BMI of the sample population. It indicates whether a person’s BMI is above or below the average value and by how many standard deviations.
Interpreting the Z-Score can reveal valuable information about the BMI data. If the Z-Score is positive, it means the individual’s BMI is above the average of the sample population. Conversely, a negative Z-Score indicates a BMI below the average. Additionally, the magnitude of the Z-Score tells us how far the individual’s BMI is from the sample average in terms of standard deviations.
For example, if we find a Z-Score of 1.5 for a particular individual, it means their BMI is 1.5 standard deviations above the average BMI of the sample population. This suggests that the individual has a higher BMI compared to their peers.
On the other hand, if we calculate a Z-Score of -0.7, it signifies that the individual’s BMI is 0.7 standard deviations below the average BMI of the sample population. This implies that the individual has a lower BMI compared to others in the sample.
In summary, the Z-Score provides a standardized measure for comparing individual BMI values to the average BMI of a sample population. It offers insights into the relative position of an individual’s BMI value within the sample and helps identify whether it is below, above, or close to the average.
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