Question

If the mean of 20 , 32 , 33 , x is 31 , find the value of x .

Answer 1

Step-by-step explanation:

Hi there!

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What is Mean?

The average of a given set of numbers is called the Arithmetic mean, or simply the mean, of the given numbers.

Mean = \frac{Sum \: of \: observations }{Number \: of \: observations }

Numberofobservations

Sumofobservations

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Coming to the question ;

Number of observations = 9

Sum of observations

= 12 + 5 + 3 + 18 + 10 + 17 + x + 6 + 6

= 77 + x

Now,

Mean = \frac{Sum \: of \: observations }{Number \: of \: observations }

Numberofobservations

Sumofobservations

⇒ 9 = \frac{77 + x }{9}

9

77+x

⇒ 9 × 9 = 77 + x

⇒ 81 = 77 + x

⇒ x = 81 - 77

⇒ x = 4

Hence, the value of x = 4.

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Range : The difference between the largest and the smallest observation is called the range of the data.

Here, largest observation = 18

And, smallest observation = 3

∴ Range = ( 18 - 3 )

⇒ Range = 15.

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Thanks for the question!

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