Question

the mean of 5 numbers is 22. if one more number is included, then the mean of the new set of numbers become 24.find the included number.

Answer 1

Answer:

The included number is 34

Step-by-step explanation:

Formula used:

$Mean=\frac{\Sigma{x}}{n}$

Let the included number be k

Given:

Mean of 5 numbers = 22

$\frac{\Sigma{x}}{5}=22$

$\Sigma{x}=22*5$

$\Sigma{x}=110$

when one more nuimber is included

$New\:\Sigma{x}=110+k$

Now,

$New\:Mean=\frac{New\:\Sigma{x}}{6}$

$24=\frac{110+k}{6}$

$24*6=110+k$

$144=110+k$

$k=34$

Therefore, the included number is 34

Answer 2

Answer:

34

Step-by-step explanation:

Mean = Total sum of all numbers/ numbers of elements in the set

In the given question, Mean = 22

Total number = 5

Hence sum of 5 numbers = 5 x 22 = 110

Now when a new number is included the sum will also increase by value of that number and total number of elements will increase by 1.

Let the included number be y. Then

Total sum = (110 + y)

Total number of elements = 6

According to question, Mean = 24

⇒ 24 = (110 + y )/6

⇒144 = 110 + y

⇒y = 34

Hence the included number is 34.