Question

The arithmetic mean of 12 observations is 7.5 the last 12 observation is 2 the mean of the first 11 observations will be
a)5.5
b)7.0
c)7.5
d)8.0

Answer 1

Answer:

Correct option is d.

Step-by-step-explanation:

From the properties of mean:

• Mean = sum of observations / number of observations

Let the 12th observation be a.

= > Mean = ( sum of first 11 observations + a ) / 12

= > 7.5 = ( sum of first 11 observations + a ) / 12

= > ( 7.5 x 12 ) = sum of first 11 observations + a

= > ( 7.5 x 12 ) - a = sum of first 11 observations

= > [ ( 7.5 x 12 ) - a ] / 11 = ( sum of first 11 observations ) / 11 { dividing both sides by 11 }

= > ( 90.0 - a ) / 11 = mean of 11 observations { sum of 11 observations / 11 represents the mean of 11 observations }

= > ( 90.0 - 2 ) / 11 = mean of first 11 observations { given, 12th observations = 2 }

= > 88.0 / 11 = mean of first 11 observations

= > 8.0 = mean of first 11 observations

Hence, correct option is d.

Answer 2

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Let's assume that Sum of the first 11 observations as x .

12th observation = 2

Now as we know that formula for average is

$\frac{sum \: of \: all \: observations}{number \: of \: observations}$

So sum of all observations will be = x + 2

Number of observations = 12

$\frac{x + 2}{12} = 7.5$

～> x + 2 = 7.5 × 12

～> x + 2 = 90

～> x = 88

So the sum of 1st 11 observations is 88 , Now mean of 11 observations will be

$\frac{88}{11} = 8$

Hence mean of first 11 observations is 8

That is option D