# Abia State Polytechnic Statistical Variance Measures Discussion

In previous units we have looked at the frequency distribution and measures of central tendency (mean, median and mode). If we rely only on these tools to describe data, what important component are we missing? What is an example of this missing component? How can you apply to health science?

Hannah Kolker posted Sep 2, 2020 4:22 PM

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Mean, median, and mode all represent measures of central tendency. They represent the center point of a dataset. Basically, the central tendency only measures one characteristic of a distribution, however, the important component that is missing is variance. Statistical variance measures how the data “distributes itself about the mean or expected value” (Kalla & Wilson, 2019). The central tendency for 2 different data sets could be 100, but one dataset could have a range of 75 to 125, while the second data set could have a range of 50 to 150. Both have the same central tendency of 100, but the variance around the center is much wider in set 2. In health science, someone going in for medical treatment would look to variance in health outcomes. For example, someone having back surgery can choose between laparoscopic or standard surgery. The patient and doctor might look to the variance of outcomes given what procedure to utilize. The patient should choose the option that has the best outcome along with the lowest variance of potential negative effects. Overall, just looking at the center of any data set, doesn’t give the entire picture and variance and standard deviation are usually required.

Reference:

Kalla, S. & Wilson, L. (2019). Statistical Variance. Retrieved form https://explorable.com/statistical-variance

Gerlinda Antoine posted Sep 2, 2020 9:15 PM

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If you rely simply on one of these components, you will not fully comprehend the data and how it can be used in your research. For example, if a set of data is collected and one only uses the mode, then we do not know what the average, or mean for that set is. The same thing goes for if you do not calculate the median. These 3 components are needed if you are going to calculate things such as IQR, lower fence, upper fence and more. For example, let us just say that you need a rotator cuff repair. Your physician’s secretary tells you that most rotator cuff repairs cost $30,000. That does not mean your case specifically will cost the same amount. That is just the mode. If she tells you that the mid price range for it is $22,000 that does not help your case either. Breaking down the numbers and understanding why they fluctuate and where the changes happen, which we tend to see in some form of a graph, will make the audience understand and relate to the information better. Using only one of these will also miss if their is an outlier in the spread of data.