The following data lists the average monthly snowfall for January in 15 cities arount the US: 29 26 6 46 17 34 15 45 19 43 37 6 9 33 37. Find the standard deviation.That is suppose to be starndard...

The following data lists the average monthly snowfall for January in 15 cities arount the US: 29 26 6 46 17 34 15 45 19 43 37 6 9 33 37.

Find the standard deviation.

That is suppose to be starndard deviation.

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lemjay | High School Teacher | (Level 3) Senior Educator

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The formula of standard deviation is:

`sigma=sqrt((sum_(i=1)^N (x_i-nu)^2)/N)`

First, solve the mean of the given values.

`nu= (29+26+6+46+17+34+15+45+19+43+37+6+9+33+37)/15`

`nu=26.8`

Then, subtract the mean from each given value. And square the result of each.

`i=1, (x_1 -nu)^2=(29-26.8)^2=4.84`     

`i=2, (x_2-nu)^2=(26-26.8)^2=0.64 `

`i=3, (x_3 -nu)^2=(6-26.8)^2= 432.64 `                                   

`i=4, (x_4 -nu)^2=(46-26.8)^2=368.64`

`i=5, (x_5 -nu)^2=(17-26.8)^2=96.04`

`i=6, (x_6 -nu)^2=(34-26.8)^2=51.84`

`i=7, (x_7 -nu)^2=(15-26.8)^2=139.24`

`i=8, (x_8 -nu)^2=(45-26.8)^2=331.24`

`i=9, (x_9 -nu)^2=(19-26.8)^2=60.84`

`i=10,(x_10 -nu)^2=(43-26.8)^2=262.44`

`i=11,(x_11 -nu)^2=(37-26.8)^2=104.04`

`i=12,(x_12 -nu)^2=(6-26.8)^2=432.64`

`i=13,(x_13 -nu)^2=(9-26.8)^2=316.84`

`i=14,(x_14 -nu)^2=(33-26.8)^2=38.44`

`i=15,(x_15 -nu)^2=(37-26.8)^2=104.04`

Then, take the sum.

 

`sum_(i=1)^N (x_i-nu)^2 =4.84+0.64+432.64+368.64+96.04+51.84+139.24`

` +331.24+60.84+262.44+104.04+432.64+316.84+38.44+104.04`

 

`sum_(i=1)^N (x_i-nu)^2=2744.4`

Then, divide this by N.

`(sum_(i=1)^N (x_i-nu))/N=2744/15=182.96`

And take the square root of it.

`sigma =sqrt((sum_(i=1)^N (x_i-nu))/N)=sqrt182.96`

`sigma=13.53`

Hence, the standard deviation of the given values is 13.53.

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