12.4 Measures of Dispersion 801 divided this number by 1 less than the number of pieces of data, − n 1. Therefore, we have Σ − − x x n ( ) 1 2 Finally, we took the square root of this value to obtain the standard deviation. Standard deviation will be used in Section 12.5 to determine the percent of data between any two values in a normal curve. Standard deviations are also often used in determining norms for a population (see Exercise 34). Standard Deviation The standard deviation, s, of a set of data can be calculated using the following formula. = Σ − − s x x n ( ) 1 2 Example 3 Determine the Standard Deviation of Stock Prices The following are the prices of nine stocks on the New York Stock Exchange. Determine the standard deviation of the prices. $17, $28, $32, $36, $50, $52, $66, $74, $104 Solution The mean, x, is = Σ = + + + + + + + + = = x x n 17 28 32 36 50 52 66 74 104 9 459 9 51 The mean is $51. Table 12.7 x x x − x x ( )2 − 17 −34 1156 28 −23 529 32 −19 361 36 −15 225 50 −1 1 52 1 1 66 15 225 74 23 529 104 53 2809 0 5836 Table 12.7 shows us that Σ − = x x ( ) 5836. 2 Since there are nine pieces of data, − = − n 1 9 1, or 8. = Σ − − = = ≈ s x x n ( ) 1 5836 8 729.5 27.01 2 The standard deviation, to the nearest hundredth, is $27.01. 7 Now try Exercise 19 Data Sets: Mean and Standard Deviation
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