Question

12. The average of a set of 3 numbers is 7 and the
average of another set of 7 numbers is 3. What is
the average of all the 10 numbers together?​

Answer 1

Working out:

In this question, we have to find the average or mean of a given data whose individual numbers are given and the total no. of observations are given.

To find Mean, we use:

$\boxed{ \bf{Average = \frac{Sum \: of \: all \: observations}{No. \: of \: obsevations} }}$

Given data in the Question,

• Average of 3 numbers = 7
• Average of next 7 numbers = 3

And we have to find the 10 numbers together.

The average of 3 numbers is 7,

⇛ Sum of all numbers = Average × No. of numbers

⇛ Sum of all numbers = 7 × 3

⇛ Sum of all numbers = 21

The average of 7 numbers is 3,

⇛ Sum of all numbers = Average × No. of numbers

⇛ Sum of all numbers = 3 × 7

⇛ Sum of all numbers = 21

⚠️ Remember, we can add the totals and the numbe rod observations to find the average of all the set of numbers, average can't be added directly to find the finally average.

Now finding the final average:

• Total sum of 10 numbers = 21 + 21 = 42
• Total no. of observations = 10

Then average of 10 numbers,

⇛ Avg. = Sum of all no. / No. of numbers.

⇛ Average = 42 / 10

⇛ Average = 4.2

So, the average of 10 numbers:

$\large{ \boxed{ \purple{ \bf{4.2}}}}$

And we are done !!

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