Question #1720b

1 Answer
Solace M.
Sep 28, 2017

Standard Deviation #~~5.3125#

Explanation:

To see an in-depth explanation, check out this answer.

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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