The average of 5 numbers is 4 .
a sixth number is added to the set which increases the mean to 7 .what is the 6th number

The sixth number is 22. Surprisingly, the exact values of the first five numbers do not matter. See the explanation.

Step-by-step explanation:

Let the sixth number be . The average of numbers is equal to the sum of these number divided by . That is:

.

Working backwards (multiply both sides by the denominator, ) to find a formula for the sum of the numbers:

.

Apply this formula to find the sum of the first five numbers:

.

If represents the value of the sixth number, the sum of the first six numbers will be equal to:

.

The average of the first six number will thus be equal to:

.

However, the question states that the average of the first six numbers is equal to . In other words,

.

Multiply both sides by the denominator, :

.

.

In other words, the sixth number is .

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