Lesson 5 Measures of Variation Solutions and Explanations

To calculate the spread of a data set, first determine the range by subtracting the smallest value from the largest. This gives a quick sense of how far apart the values are, but it doesn’t account for outliers.

Next, calculate the mean of the data. Then, for each number, subtract the mean and square the result. Afterward, average these squared differences to find the variance, which indicates the overall spread of the data points around the mean.

Finally, to interpret this more easily, take the square root of the variance to obtain the standard deviation. This measure, expressed in the same units as the data, provides a clear indication of how spread out the data is, helping to understand patterns or inconsistencies.