Question

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 1

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