Problem

Find the range and standard deviation of the set of data. \[ \text { .12, 9, 6, 12, } 16 \text { 믄 } \] The range is 10 . (Simplify your answer.) The standard deviation is (Round to the nearest hundredth as needed.)

Solution

Step 1 :First, we need to calculate the range of the data set. The range is the difference between the highest and lowest values in the set. In this case, the highest value is 16 and the lowest value is .12. So, the range is 16 - .12 = 15.88.

Step 2 :Next, we need to calculate the standard deviation. The standard deviation is a measure of how spread out the numbers in the data set are. It is calculated by taking the square root of the variance. The variance is the average of the squared differences from the mean.

Step 3 :First, we calculate the mean (average) of the data set. Then, for each number in the data set, we subtract the mean and square the result. We then find the average of these squared differences. Finally, we take the square root of the variance to get the standard deviation.

Step 4 :The range of the data set is \(\boxed{15.88}\) and the standard deviation is \(\boxed{6.02}\).

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Source: https://solvelyapp.com/problems/16724/

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