Question

The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers​

Answer 1

Given : Mean of three numbers is 10 & Mean of other four numbers is 12.

Need to find : Mean of all the numbers .

___________________

$\sf {\underline{\pink{According~ to ~ the~ Question}}}$

Mean of three numbers = 10

Total of three numbers = 3 × 10

Total of three numbers = 30

Mean of four other numbers is 12

Total of four numbers = 4 × 12

Total of four numbers = 48

Total Number of Elements = 3 + 4 = 7

Sum of all elements = 30 + 48 = 78

Now, calculating the mean of all numbers

$\\ \star{\boxed{\purple{\sf{Mean = \frac{Sum \: of \: all \: elements}{Total \: number \: of \: elements \: } }}}}$

substituting the value we get

$\implies \tt \: Mean \: = \frac{78}{7} \\ \\ \implies \tt \: Mean \: = \cancel \frac{78}{7} \\ \\ \implies \tt mean \: = 11.14$

• $\\ {\boxed{{\sf{Hence , \: the \: mean \: of \: total \: number \: is \: 11.41}}}}$

Answer 2

Answer:

Given :-

• The mean of three numbers is 10.
• The mean of other four numbers is 12.

To Find :-

• What is the mean of all the numbers.

Formula Used :-

$\clubsuit$ Mean Formula :

$\small \bigstar \: \: \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: Of\: Observations}{Total\: Number\: Of\: Observations}}}}\: \: \: \bigstar$

Solution :-

First, we have to find the sum of observations :

$\bigstar$ The mean of three numbers is 10.

So,

$\implies \bf Sum\: of\: three\: numbers =\: 10$

$\implies \sf Total\: Numbers =\: 3 \times 10$

$\implies \sf\bold{\green{Total\: Numbers =\: 30}}$

Again,

$\bigstar$ The mean of other four numbers is 12.

So,

$\implies \sf Sum\: of\: four\: numbers =\: 12$

$\implies \sf Total\: Numbers =\: 4 \times 12$

$\implies \sf\bold{\green{Total\: Numbers =\: 48}}$

Hence, the sum of observations is :

$\implies \sf Sum\: of\: Observations =\: 30 + 48$

$\implies \sf\bold{\blue{Sum\: of\: Observations =\: 78}}$

Now, we have to find the total number of observations :

$\small \implies \sf Total\: Number\: of\: Observations =\: 3 + 4$

$\small \implies \sf\bold{\blue{Total\: Number\: of\: Observations =\: 7}}$

Now, we have to find the mean of all the numbers :

Given :

• Sum of Observations = 78
• Total Number of Observations = 7

According to the question by using the formula we get,

$\small \dashrightarrow \bf Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}$

$\dashrightarrow \sf Mean =\: \dfrac{78}{7}$

$\dashrightarrow \sf\bold{\red{Mean =\: 11.14}}$

$\sf\bold{\purple{\underline{\therefore\: The\: mean\: of\: all\: the\: numbers\: is\: 11.14\: .}}}$

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