Question

Looking for the point estimate for the population standard deviation

Answer 1

Given

Random sample

10 , 34 , 38 , 36 , 18 , 26 , 7 , 12 , 18 , 33

Find

Point estimate for the population standard deviation.

Step-by-step explanation

standard deviation is given by

`\sigma=\sqrt{(1)/(n-1)\sum_(i=1)^n}(x_i-\bar{X})^2`

first we find the mean ,

`\begin{gathered} \bar{X}=(10+34+38+36+18+26+7+12+18+33)/(10) \\ \\ \bar{X}=(232)/(10)=23.2 \end{gathered}`

put the values of each in standard deviation formula

on solving we obtain ,

`\begin{gathered} \sigma=√(121.96) \\ \sigma=11.04 \end{gathered}`

Final Answer

Therefore , the point estimate for the population standard deviation is 11.04