Question

For the following set of data, find the sample standard deviation, to the nearest thousandth.77, 124, 77, 82, 100, 139, 81

Answer 1

Sample standard deviation:

`s=\sqrt{\frac{\Sigma(x_i-\bar{x})^2}{n-1}}`

To find the standard deviation of the given set:

1. Fidn the mean:

`\bar{x}=(77+124+77+82+100+139+81)/(7)=(680)/(7)\approx97.14`

2. Find the (x-mean) for each data:

`\begin{gathered} (77-97.14)=-20.14 \\ (124-97.14)=26.86 \\ (77-97.14)=-20.14 \\ (82-97.14)=-15.14 \\ (100-97.14)=2.86 \\ (139-97.14)=41.86 \\ (81-97.14)=-16.14 \end{gathered}`

3. Square the results you get in previous step:

`\begin{gathered} (-20.14)\placeholder{⬚}^2=405.6196 \\ 26.86^2=721.4596 \\ (-20.14)\placeholder{⬚}^2=405.6196 \\ (-15.14)\placeholder{⬚}^2=229.2196 \\ 2.86^2=8.1796 \\ 41.86^2=1752.2596 \\ (-16.14)\placeholder{⬚}^2=260.4996 \end{gathered}`

4. Add the squares you get in previus step:

`405.6196+721.4596+405.6196+229.2196+8.1796+1752.2596+260.4996=3782.8572`

5. Divide the resull above into n-1:

`(3782.8572)/(7-1)=(3782.8572)/(6)=630.4762`

6. Find the square root of the quotient you get in previous step:

`s=√(630.4762)\approx25.109`

Then, the standard deviation is 25.109