Question

The mean of 11 numbers is 42 if the mean of the first no. Is 37 and that of the last 6 numbers is 46 find the 6th number

Answer 1

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

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Answer 2

$\underline{\bold{Solution:-}}$

Mean of 11 numbers = 42

Sum of these 11 numbers = mean of 11 numbers × 11

= 42 × 11

= 462

Mean of first 6 numbers = 37

Sum of first 6 numbers = 37 × 6 = 222

Mean of last 6 numbers = 46

Sum of last 6 numbers = 46 × 6 = 276

We know that

Sixth term = [Sum of first 6 terms + Sum of last 6 terms] - sum of all 11 terms

$sixth \: term \: = (222 + 276) - 462 \\ \\ sixth \: term \: =496 - 462 \\ \\ \boxed{\bold{sixth \: term \: =34}}$

So, the sixth term is 34.