Question

Find the average of all integers between -11 and+7 that are divisible by 2 or3

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• Integers between - 11 to + 7

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Average of integers which are divisible by 2 or 3.

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

First,

• The integers that are divisible by 2 between - 11 to + 7,

• - 10, - 8, - 6, - 4, - 2, 0, + 2, + 4, + 6

• The integers that are divisible by 3 between - 11 to + 7,

• - 9, - 6, - 3, 0, + 3, + 6

Now,

• Total observations =

• - 10, - 9, - 8, - 6, - 6, - 4, - 3, - 2, 0, 0, + 2, + 3, + 4, + 6, + 6

• Total number of observations = 15

Now,

We know that,

$\boxed{\pink{\sf Average \: = \: \dfrac{Given \: observations}{Total \: number \: of \: observations}}}$

Substituting the values,

• Average =

$\sf \dfrac{- 10 \: - 9 \: - 8 \: - 6 \: - 6 \: - 4 \: - 3 \: - 2 \: + \: 0 \: + \: 0 \: + 2 \: + 3 \: + 4 \: + 6 \: + 6}{15}$

• Average = $\sf \dfrac{- \: 27}{15}$

• Average = - 1.8

Therefore,

• Average of all integers that are between - 11 and + 7 and divisible by 2 and 3 is - 1.8.