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What is the standard deviation of -3,0,3,6,9

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Final answer:

The standard deviation of the dataset -3,0,3,6,9 is 4.71. Mean is calculated first, deviations are squared, averaged, and the square root of this average gives the standard deviation.

Step-by-step explanation:

The standard deviation of the numbers -3,0,3,6,9 is 4.71.

To calculate the standard deviation, first find the mean (average) of the data set. Add the numbers together and divide by the quantity of the numbers. For the data set (-3,0,3,6,9), the mean is ( -3 + 0 + 3 + 6 + 9 ) / 5 = 15 / 5 = 3. Next, subtract the mean from each number to get the deviation for each number: -3 - 3 = -6, 0 - 3 = -3, 3 - 3 = 0, 6 - 3 = 3, and 9 - 3 = 6.

Now square each of these deviations: (-6)^2 = 36, (-3)^2 = 9, (0)^2 = 0, (3)^2 = 9, (6)^2 = 36. The sum of these squares is 36 + 9 + 0 + 9 + 36 = 90. Divide this sum by the number of values minus one to get the variance: 90 / (5 - 1) = 22.5. Finally, take the square root of the variance to get the standard deviation, which is roughly 4.71.

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