Question

The mean of a set of 12 observations is 10 and
another set of 8 observations is 12. The mean of
combined set is ?​

Answer 1

Question :

The mean of a set of 12 observations is 10 and  another set of 8 observations is 12.The mean of  combined set is ?​

Answer :

The mean of combined set = 10.8

Given :

• The mean of a set of 12 observations is 10
• The mean of another set of 8 observations is 12

To find :

• The mean of combined set

Solution :

    We know,

      $\boxed{\bf \implies Mean =\frac{Sum \ of \ observations}{No.of \ observations}}$

 ⇒ The mean of set of 12 observations = 10

       

          $\frac{Sum \ of \ 12 \ observations}{12} =10 \\\\ Sum \ of \ 12 \ observations=10 \times 12 \\\\ Sum \ of \ 12 \ observations=120$

 ⇒ The mean of set of 8 observations = 12

           $\frac{Sum \ of \ 8 \ observations}{8} =12 \\\\ Sum \ of \ 8 \ observations=12 \times8\\\\Sum \ of \ 8 \ observations=96$

⇒ The mean of combined set :

         Sum of observations = Sum of 12 observations + Sum of 8 observations

                                             = 120 + 96

                                             = 216

         No. of observations = 12 + 8

                                             = 20

     $\text{Mean of combined set = } \frac{\text{Sum of observations}}{\text{No.of observations}} \\\\ \text{Mean of combined set = } \frac{216}{20} \\\\ \text{Mean of combined set = } \frac{108}{10} \\\\ \text{Mean of combined set = }=10.8$

║ Mean of combined set = 10.8