Range, Standard Deviation, and Variance

From the above dotplots can you order the data sets A, B, C, D in order from least variation to most variation (that is from least spread out to most spread out).

We can find the range of these data sets by taking the largest number and subtracting the smallest number. What is the range of these data sets?

Notice how all four data sets have the same range despite some being more spread out than others. Range is a basic way to describe variation in data, but we need more advanced measurements. We will use technology to measure standard deviations and variance. What are three ways we can measure variation?

The standard deviation of a data set is a measure of variation based on how far each data value deviates, or is different, from the mean. The standard deviation

• is never negative.
• is zero if all the data values are equal, and will get larger as the data spreads out.
• has the same units as the original data.
• can be highly influenced by outliers, similar to the mean.