Answer:
(a) σ² = 144
(b) s² = 12
Step-by-step explanation:
(a) Population variance σ² = ∑(X - [tex]\overline{X}[/tex])² / N
The arithmetic mean [tex]\overline{X} = \frac{8 + 17 + 29 + 35 + 41}{5}[/tex]
[tex]\overline{X} = \frac{130}{5}[/tex]
[tex]\overline{X} = 26[/tex]
σ² = [tex]\frac{(8 - 26)^{2} + (17 - 26)^{2} + (29 - 26)^{2} + (35 - 26)^{2} + (41 - 26)^{2}}{5}[/tex]
= [tex]\frac{(- 18)^{2} + (- 9)^{2} + (3)^{2} + (9)^{2} + (15)^{2}}{5}[/tex]
= [tex]\frac{324\ +\ 81\ +\ 9\ +\ 81\ +\ 225}{5}[/tex]
= [tex]\frac{720}{4}[/tex]
σ² = 144
(b) [tex]Standard\ deviation = \sqrt{Variance}[/tex]
[tex]= \sqrt{144}[/tex]
= 12
