Each data value deviates from the mean. In other words, each value differs from the mean. Data values with large deviations (i.e., those that differ farther from the mean) contribute more to the variability in the data set. Values with small deviations do not contribute as much to the total variability. To measure total variability, we need a way to summarize these deviations. 5 How can we summarize the deviations to obtain a single number that describes the typical deviation from the mean for all values in a data set? Take a minute to consider this on your own first before sharing in your group. The standard deviation is a measure of variability that describes the average deviation from the mean for all values in a data set. To find the standard deviation of a sample, we (1) square each deviation, (2) find the sum of the squared deviations, (3) find the average of the squared deviations, and (4) take the square root of the average of the squared deviations. 6 Your instructor will assign you one of the samples to analyze. For the sample that you are assigned, complete the table below. A Enter in the deviations and compute the squared deviations. For the squared deviations, keep two places after the decimal. Tampa Bay Rays Value Deviation (Deviation)2 1 2.8 3.2 5.6 8 8