ondreduty1789

17.05.2021 •

Mathematics

PLEASE HELP I WILL GIVE BRAINLIEST HELP ME PLEASE I WILL GIVE BRAINLIEST! look in attatchment below

PLEASE HELP I WILL GIVE BRAINLIEST HELP ME PLEASE I WILL GIVE BRAINLIEST!

look in attatchment bel

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Ответ:

nforrestall

20.02.2023

Mathematics

a) The third quartile Q₃ = 56.45

b) Variance $\mathbf{ \sigma^2 =2633.31}$

Step-by-step explanation:

Given that :

Q_1 = 30.8

Median Q_2 = 48.5

Mean = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

$SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}$

$-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}$

-0.38Q_3 + 11.704 = Q_3 +30.8 - 97

1.38Q_3 = 77.904

Divide both sides by 1.38

Q_3 = 56.45

b) The objective here is to determine the approximate value of the variance;

Using the relation

$SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}$

$-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}$

$-0.38= \dfrac{(-19.5) }{\sigma}$

$-0.38* \sigma = {(-19.5) }{}$

$\sigma =\dfrac {(-19.5) }{-0.38 }$

$\sigma =51.32$

Variance = $\sigma^2 =51.32^2$

$\mathbf{ \sigma^2 =2633.31}$

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