Question

The mean of a set of 10 numbers is 50. When a number x is added to the set, the mean is changed to 52. Find the value of x.

Answer 1

Let the sum of the ten numbers be "a" and the new number added be "b"

Mean = a/10

a/10 = 50

=> a = 500 ------(1)

When new number is added

Mean = 50

=> (a+b)/ 11 = 50

=> a + b = 550

=> 500 + b = 550

=> b = 550 - 500

=> b = 50

The number that is added is 50

:)

Answer 2

The value of x = 72

Given :

• The mean of a set of 10 numbers is 50.

• When a number x is added to the set, the mean is changed to 52.

To find :

The value of x

Solution :

Step 1 of 2 :

Form the equation to find the value of x

The mean of a set of 10 numbers is 50

∴ Sum of 10 numbers

= 50 × 10

= 500

When a number x is added to the set , then total numbers in the set = 10 + 1 = 11

As the mean is changed to 52

∴ Sum of 11 numbers

= 52 × 11

= 572

By the given condition

500 + x = 572

Step 2 of 2 :

Find the value of x

500 + x = 572

⇒ x = 572 - 500

⇒ x = 72

Hence the required value of x = 72

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