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marishachu [46]
3 years ago
11

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 =
Mathematics
1 answer:
Nuetrik [128]3 years ago
7 0

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

 

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As the probabilities add up to 1, so the condition 2 is also satisfied.

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