Question

18. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean
of 20 of them is 11. The last two numbers are 10.
Solution:​

Answer 1

Answer:

• The mean of the 32 numbers is 12.1875.

Step-by-step explanation:

Given that:

• Total number = 32
• The mean of 10 of them is 15 and the mean of 20 of them is 11.
• The last two numbers are 10.

To Find:

• The mean of the 32 numbers.

Formula used:

• Mean = (Sum of observations)/(Number of observations)

Finding the sum of observations of 10 numbers:

⟶ 15 = (Sum of observations)/10

⟶ Sum of observations = 15 × 10

⟶ Sum of observations = 150

Finding the sum of observations of 20 numbers:

⟶ 11 = (Sum of observations)/20

⟶ Sum of observations = 11 × 20

⟶ Sum of observations = 220

Finding the sum of observations of 32 numbers:

⟶ Sum of observations = 150 + 220 + 10 + 10

⟶ Sum of observations = 390

Finding the mean of the 32 numbers:

We have.

• Number of observations = 32
• Sum of observations = 390

⟶ Mean = 390/32

⟶ Mean = 12.1875

∴ Mean of the 32 numbers = 12.1875

Answer 2

Answer:

Given :-

• The mean of 10 of them is 15 and the mean of 20 of them is 11.
• The last two numbers are 10.

To Find :-

• What is the mean of the 32 numbers.

Formula Used :-

$\clubsuit$ Mean Formula :

$\longmapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: number\: of\: Observations}}}}$

Solution :-

First, we have to find the sum of observations of 10 number :

Given :

• Mean = 15
• Total number of observations = 10

According to the question by using the formula we get,

$\implies \sf 15 =\: \dfrac{Sum\: of\: Observations}{10}$

By doing cross multiplication we get,

$\implies \sf Sum\: of\: observations =\: 10(15)$

$\implies \sf Sum\: of\: observations =\: 10 \times 15$

$\implies \sf\bold{\green{Sum\: of\: observations =\: 150}}$

Hence, the sum of observations is 150.

Again, we have to find the sum of observations of 20 number:

Given :

• Mean = 11
• Total number of observations = 20

According to the question by using the formula we get,

$\implies \sf 11 =\: \dfrac{Sum\: of\: Observations}{20}$

By doing cross multiplication we get,

$\implies \sf Sum\: of\: observations =\: 20(11)$

$\implies \sf Sum\: of\: observations =\: 20 \times 11$

$\implies\sf\bold{\green{Sum\: of\: observations =\: 220}}$

Now, we have to find the sum of observations 32 numbers:

$\implies \sf Sum\: of\: observations =\: 150 + 220 + 10 + 10$

$\implies \sf Sum\: of\: observations =\: 370 + 20$

$\implies \sf\bold{\purple{Sum\: of\: observations =\: 390}}$

Now, we have to find the mean of the 32 numbers:

Given :

• Sum of observations = 390
• Total number of observations = 32

According to the question by using the formula we get,

$\implies \sf Mean =\: \dfrac{\cancel{390}}{\cancel{32}}$

$\implies \sf Mean =\: \dfrac{\cancel{195}}{\cancel{16}}$

$\implies \sf \bold{\red{Mean =\: 12.1875}}$

$\therefore$ The mean of the 32 numbers is 12.1875.