Given
Random sample
10 , 34 , 38 , 36 , 18 , 26 , 7 , 12 , 18 , 33
Find
Point estimate for the population standard deviation.
Explanation
standard deviation is given by
[tex]\sigma=\sqrt{\frac{1}{n-1}\sum_{i=1}^n}(x_i-\bar{X})^2[/tex]
first we find the mean ,
[tex]\begin{gathered} \bar{X}=\frac{10+34+38+36+18+26+7+12+18+33}{10} \\ \\ \bar{X}=\frac{232}{10}=23.2 \end{gathered}[/tex]
put the values of each in standard deviation formula
on solving we obtain ,
[tex]\begin{gathered} \sigma=\sqrt{121.96} \\ \sigma=11.04 \end{gathered}[/tex]
Final Answer
Therefore , the point estimate for the population standard deviation is 11.04
