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ehidna [41]
3 years ago
8

What is the mean, variance, and standard deviation of the values? Round to the nearest tenth. 1,9,4,12,13,13

Mathematics
1 answer:
tankabanditka [31]3 years ago
8 0

To compute the mean, you simply have to sum all the elments in the data set and the divide the sum by the number of elements:


M = \frac{1+4+9+12+13+13}{6} = \frac{52}{6} = 8.6


To compute the variance, we first need to compute the distance of each element from the mean. To do so, we build a "parallel" dataset, given by the difference of every value and the mean:


D' = 1-8.6,9-8.6,4-8.6,12-8.6,13-8.6,13-8.6


D' = -7.6, 0.4, -4.6, 3.4, 4.4, 4.4


Now we need those difference squared:


(D')^2 = 57.76, 0.16, 21.16, 11.56, 19.36, 19.36


The variance is the mean of this new vector, so


\sigma^2 = \frac{57.76+ 0.16+ 21.16+ 11.56+ 19.36+ 19.36}{6} = \frac{129.36}{6} = 21.6


Finally, the standard deviation is simply the square root of the variance, so you have


\sigma = \sqrt{21.6} = 4.6

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