Question

The average of 7 numbers is 5. if the average of first six of these numbers is 4, the seventh number is

Answer 1

Answer:

The seventh number is 11

Step-by-step explanation:

Given data

The average of 7 numbers  = 5

the average of first 6 of these numbers = 4

here we need to find 7th number    

Let x₁ x₂ x₃ x₄ x₅ x₆ x₇   be the 7 numbers  

given average of 7 numbers  =  $\frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6}+x_{7} }{7}$  = 5

x₁ + x₂+x₃ + x₄ + x₅ + x₆ + x₇  = 7(5)  

x₁ + x₂+x₃ + x₄ + x₅ + x₆ + x₇  = 35 _ (1)    

and average of first 6 numbers = $\frac{x_{1} + x_{2}+ x_{3} +x_{4} +x_{5}+ x_{6} }{6}$  = 4  

x₁ + x₂ + x₃ + x₄ + x₅ + x₆  = 4(6)

x₁ + x₂ + x₃ + x₄ + x₅ + x₆  = 24 _ (2)  

substitute (2) in (1)

⇒   24 + x₇ = 35

⇒   x₇  = 35 - 24 = 11

⇒ required 7th number = 11    

Answer 2

The seventh number is 11.

Given:

• The average of 7 numbers is 5.
• if the average of first six of these numbers is 4.

To find:

• Find the seventh number

Solution:

Formula\Concept to be used:

Average= Sum of numbers/ Total numbers.

Step 1:

Put the values in the formula and find the sum of all seven numbers.

As,

Average =5

Total numbers = 7.

$5 = \frac{ \text{sum \: of \: numbers}}{7}$

or

Sum of numbers =5×7= 35

Step 2:

Put the values in the formula and find the sum of first six numbers.

As,

Average = 4

Total numbers= 6

Sum of first six numbers =4×6

Sum of first six numbers =24

Step 3:

Find the seventh number.

Subtract the results of both steps.

7th number= Sum of seven numbers-Sum of first six numbers

7th number= 35-24

7th number= 11

Thus,

7th number is 11.

Learn more:

1) If the mean of 2,5,8,x,5,6,is 6 then find value of x.

https://brainly.in/question/2360617

2) The mean of 45 numbers is 25 if each number is multiplied by 3 find the new mean

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