Measures of dispersion describe how spread out or clustered the data is. The range is the difference between the highest and lowest values. Standard deviation measures how far each value deviates from the mean by finding the deviations, squaring them, summing them, dividing by n-1, and taking the square root. It accounts for all data points unlike the range. To calculate standard deviation, first find the mean, then deviations from it, square those values, sum them, and divide the sum by n-1 before taking the square root.

1. 12.3 Measures of Dispersion

2. RangeThe difference between the highest and lowest data valuesRange = highest – lowest

3. Example 1Find the range for a set of data:A. 10, 20, 30, 40, 50B. 84, 30, 90, 59, 67, 29

4. Standard DeviationDependent on all of the data itemsFound by determining how each value deviates (or differs) from the mean

5. Computing the standard deviation for a data set1. Find the mean of the data items.2. Find the deviation of each data from the mean data item – mean3. Square each deviation (data item – mean) 24. Sum the squared deviations ∑ (data item – mean) 2

6. Cont…5. Divide the sum by n-1 where n represents the number of items.∑ (data item – mean) 2 n-16. Take the square root of the answer. √ ∑ (data item – mean) 2n-1