M3A4 Lab (Chebyshev’s Theorem)
Chebyshev’s Theorem states that in any given data set or list of values, whether it is a population, or a sample of that population, the data will fall in a certain percentage in relation to the average or mean of the values. More specifically, it shows that in the given data set, at least
75% of the data will fall within 2 standard deviations on either side of the mean. The standard deviation is the way we describe how data spreads around the mean. In the same set of data, at least 88.9 % of the data will fall within 3 standard deviations on either side of the mean, and finally at least 93.8 % of the data will fall within 4 standard deviations on either side of the mean. It is easier to see if you look at the data in a chart such a sample that has data which is evenly distributed such as that which is seen in a Bell Shaped Curve. Here, I will draw you a picture so you can see what it looks like.

Now, when you look at the graph you can see where the median is. You can see where the values of the standard deviation are, and you can see where each percentage of values will in relation to the mean. Notice the Orange line represents 75% of the data; the Green line represents 88.9% of the data, and the Yellow line represents 93.8% of data. I hope that helps you to understand what
Chebyshev’s Theorem says and what it means.

Yes, you would be right because Chebyshev’s Theorem can be used in any population or any sample of a population. Even if the data is not distributed evenly, there is still a certain percentage of data that will fall within a certain distance from the mean of the data. The definition of the data spread around the mean is often expressed as any data set and for any constant (k) greater than 1, the percentage of that must lie within k standard deviations on either side of the