True or false? "In any sample data set, the sum of all the values is equal to the product of the mean and the sample size."

The statement is true because, by definition, the mean of a sample is calculated by dividing the sum of all the values in that sample by the number of values (the sample size). Therefore, if you rearrange this formula, the sum of the values can be expressed as the product of the mean and the number of values.

Mathematically, if ( \text{mean} = \frac{\text{sum of values}}{\text{sample size}} ), then by multiplying both sides by the sample size, you obtain ( \text{sum of values} = \text{mean} \times \text{sample size} ). This ensures that every time you take the mean of a dataset and multiply it by the number of items in that dataset, you will indeed equal the total of those items.

This foundational concept is essential in statistics, as it helps researchers and analysts understand relationships in data and reinforces the idea that the mean summarizes a dataset regarding its total size and content.