Question #1720b

1 Answer
Solace M.
Sep 28, 2017

Standard Deviation ~~5.3125

Explanation:

To see an in-depth explanation, check out [this answer.](https://socratic.org/questions/the-following-data-show-the-number-of-hours-of-sleep-attained-during-a-recent-ni#481033)

First we find the mean , which is
(2.2+10.7+5.4+16.3+12.1+1.8+2.6)/7
=51.1/7

=7.3.

Next we find the variance. What we do is we take one number from the data set, subtract it from the mean, then square the result, like so:
(2.2-7.3)^2
=(-5.1)^2

= 26.01

We do this for the rest of the numbers, to get
(10.7-7.3)^2=11.56
(5.4-7.3)^2=3.61
(16.3-7.3)^2=81
(12.1-7.3)^2=23.04
(1.8-7.3)^2=30.25
(2.6-7.3)^2=22.09

We now add them together and divide them by how many there are, so
(26.01+11.56+3.61+81+23.04+30.25+22.09)/7
=197.56/7

=4939/175~~28.22285714

The last step is to find the standard deviation, which we get by finding the square root of the variance, so
sqrt(4939/175)~~5.3125

I hope I helped!

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