Question

Find the population variance and standard deviation. 8​, 17​, 29​, 35​, 41 Choose the correct answer below. Fill in the answer box to complete your choice.
a. sigma^2 =
b. s^2 =

Answer 1

Answer:

(a) σ²  = 144

(b) s² = 12

Step-by-step explanation:

(a) Population variance σ² = ∑(X - $\overline{X}$)² / N

The arithmetic mean $\overline{X} = \frac{8 + 17 + 29 + 35 + 41}{5}$

                                   $\overline{X} = \frac{130}{5}$

                                   $\overline{X} = 26$

σ²  =  $\frac{(8 - 26)^{2} + (17 - 26)^{2} + (29 - 26)^{2} + (35 - 26)^{2} + (41 - 26)^{2}}{5}$

     =  $\frac{(- 18)^{2} + (- 9)^{2} + (3)^{2} + (9)^{2} + (15)^{2}}{5}$

     =  $\frac{324\ +\ 81\ +\ 9\ +\ 81\ +\ 225}{5}$

     = $\frac{720}{4}$

σ²  = 144

(b) $Standard\ deviation = \sqrt{Variance}$

                                   $= \sqrt{144}$

                                   = 12