Question #1720b

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Question #1720b

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Answer 1 · 2017-09-28T09:38:43

Standard Deviation $\approx 5.3125$ $~~5.3125$

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
$\frac{2.2 + 10.7 + 5.4 + 16.3 + 12.1 + 1.8 + 2.6}{7}$ $(2.2+10.7+5.4+16.3+12.1+1.8+2.6)/7$
$= \frac{51.1}{7}$ $=51.1/7$

$= 7.3$ $=7.3$ .

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:
${(2.2 - 7.3)}^{2}$ $(2.2-7.3)^2$
$= {(- 5.1)}^{2}$ $=(-5.1)^2$

$= 26.01$ $= 26.01$

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

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

$= \frac{4939}{175} \approx 28.22285714$ $=4939/175~~28.22285714$

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

I hope I helped!

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Question #1720b

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