Question

Q. 8. The mean of ten numbers is 58. If one of the numbers is 40, what is the
mean of the other nine?​

Answer 1

Answer:

• Mean of the other nine numbers is 60.

Step-by-step explanation:

Given that:

• The mean of ten numbers is 58.
• One of the numbers is 40.

To Find:

• What is the mean of the other nine numbers?

Formula used:

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

When there is ten numbers:

• Mean = 58
• Number of observations = 10

Finding the sum of observations:

⟶ 58 = (Sum of observations)/10

⟶ Sum of observations = 58 × 10

⟶ Sum of observations = 580

When there is nine numbers:

Sum of observations = Sum of 10 numbers - One number

⟶ Sum of observations = 580 - 40

⟶ Sum of observations = 540

Now we have:

• Sum of observations = 540
• Number of observations = 9

Finding the mean of the other nine numbers:

⟶ Mean = 540/9

⟶ Mean = 60

∴ Mean of the other nine numbers = 60

Answer 2

Answer:

Given :-

• The mean of ten numbers is 58.
• One of the numbers is 40.

To Find :-

• What is the mean of other nine.

Formula Used :-

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

Solution :-

$\mapsto$ The mean of ten numbers is 58, it means :

• Mean = 58
• Total number of observations = 10

According to the question by using the formula we get,

$\implies \sf 58 =\: \dfrac{Sum\: of\: observations}{10}$

By doing cross multiplication we get,

$\implies \sf Sum\: of\: observations =\: 10 \times 58$

$\implies \sf\bold{\green{Sum\: of\: observations =\: 580}}$

Hence, the sum of observations is 580.

Again,

$\mapsto$ One of the numbers is 40,

Then,

$\implies \sf Sum\: of\: observations =\: 580 -\: 40$

$\implies \sf\bold{\purple{Sum\: of\: observations =\: 540}}$

Now, we have to find the mean of the other nine :

Given :

• Sum of observations = 540
• Total number of observations = 9

According to the question by using the formula we get,

$\implies \sf Mean\: of\: other\: nine =\: \dfrac{\cancel{540}}{\cancel{9}}$

$\implies \sf\bold{\red{Mean\: of\: other\: nine =\: 60}}$

$\therefore$ The mean of other nine is 60.