What does Chebyshev's Theorem state about data values within two standard deviations of the mean?

Chebyshev's Theorem provides a general rule for the distribution of data points in any dataset, regardless of its shape. Specifically, the theorem states that for any distribution, at least a certain percentage of values will lie within a specified number of standard deviations from the mean.

According to the theorem, at least 75% of the data values will be found within two standard deviations of the mean. This means that when you calculate the mean and standard deviation of a dataset, if you look at the range defined by two standard deviations above and below the mean, you can be confident that at least 75% of all data values will fall within this range.

This theorem is particularly useful because it applies to both normal and non-normal distributions. Thus, it provides a flexible tool for understanding data sets where the distribution shape is unknown.

The percentage stated in the other choices does not align with the theorem's conclusions; hence they do not represent the correct interpretation of Chebyshev's Theorem. This understanding of the properties of statistical distributions is vital for accurately interpreting data and applying statistical methods effectively.