Question

The mean of the six observation 5,15,25,35,45,55 is 30 find the variances

Answer 1

Given :- The mean of the six observation 5,15,25,35,45,55 is 30 find the variances .?

Answer :-

mean = 30

so,

→ sumof (difference)² = (30 - 5)² + (30 - 15)² + (30 - 25)² + (30 - 35)² + (30 - 45)² + (30 - 55)² = 25² + 15² + 5² + (-5)² + (-15)² + (-25)² = 2*625 + 2*225 + 2*25 = 1250 + 450 + 50 = 1750 .

then,

→ variance = sum of (difference)² / number of observation .

→ variance = 1750 / 6 = 291.67 (Ans.)

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Answer 2

SOLUTION

GIVEN

The mean of the six observation 5 , 15 , 25 , 35 , 45 , 55 is 30

TO DETERMINE

The variance

CONCEPT TO BE IMPLEMENTED

For a given set of n observations

$\sf{ \{x_1,x_2,...,x_n \} }$

If mean

$\sf{ = \overline{x}}$

Then variance

$\displaystyle \sf{ = \sum \: \frac{ {( x_i - \bar{x} )}^{2} }{n} }$

EVALUATION

Here it is given that mean of the six observation 5 , 15 , 25 , 35 , 45 , 55 is 30

Hence

Number of observations = 6

Observations are 5,15,25,35,45,55

Mean = 30

Hence the required variance

$\displaystyle \sf{ = \sum \: \frac{ {( x_i - \bar{x} )}^{2} }{n} }$

$\displaystyle \sf{ = \frac{ {(5 - 30)}^{2} + {(15 - 30)}^{2} +{(25 - 30)}^{2} +{(35 - 30)}^{2} +{(45 - 30)}^{2} +{(55 - 30)}^{2} }{6} }$

$\displaystyle \sf{ = \frac{ {( - 25)}^{2} + {( - 15)}^{2} +{( - 5)}^{2} +{(5)}^{2} +{(15 )}^{2} +{(25)}^{2} }{6} }$

$\displaystyle \sf{ = \frac{ 625 + 225+25 +25 +225 +625 }{6} }$

$\displaystyle \sf{ = \frac{ 1750 }{6} }$

= 291.67

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