the average age of the sixth students is 11 years.If two students of a

1.	the average age of the sixth students is 11 years.If two students of age 14 and 16 years join ,then what will be their average age?
Answer» Answer : AVERAGE age = 12 years Step-by-step explanation : $\underline{\underline{\bf Average :}}$ ⇒ Add up all the TERMS and divide the number of terms in the data set. ⇒ The average of x₁, x₂, x₃ ,..., xₙ $Average=\frac{x_1+x_2+x_3+...+x_n}{n}$ we know, $\boxed{\bf Average=\frac{sum \ of \ observations}{number \ of \ observations}}$ The average age of the six students is 11 years number of observations = 6 $\bf \frac{sum \ of \ six \ students' \ age}{6} =11 \\\\ sum \ of \ six \ students' \ age=11\times6 \\\\ sum \ of \ six \ students' \ age=66$ If two students of age 14 and 16 years JOIN, number of observations = 8 $Average \ age= \bf \frac{sum \ of \ six \ students' \ age+14+16}{8}$ $\bf =\frac{66+14+16}{8} \\\\ \bf =\frac{96}{8} \\\\ =12 \ years$ ∴ If two students of age 14 and 16 years join, then their average age = 12 years

the average age of the sixth students is 11 years.If two students of age 14 and 16 years join ,then what will be their average age?

Answer»

AVERAGE age = 12 years

$\underline{\underline{\bf Average :}}$

⇒ Add up all the TERMS and divide the number of terms in the data set.

⇒ The average of x₁, x₂, x₃ ,..., xₙ

$Average=\frac{x_1+x_2+x_3+...+x_n}{n}$

we know,

$\boxed{\bf Average=\frac{sum \ of \ observations}{number \ of \ observations}}$

number of observations = 6

$\bf \frac{sum \ of \ six \ students' \ age}{6} =11 \\\\ sum \ of \ six \ students' \ age=11\times6 \\\\ sum \ of \ six \ students' \ age=66$

number of observations = 8

$Average \ age= \bf \frac{sum \ of \ six \ students' \ age+14+16}{8}$

$\bf =\frac{66+14+16}{8} \\\\ \bf =\frac{96}{8} \\\\ =12 \ years$

∴ If two students of age 14 and 16 years join,

then their average age = 12 years