Question

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number.

Answer 1

29

Explanation:

Let a12 be the mean of the first 12 numbers:

a12=(sumOf12Numbers)/12.

So, sumOf12Numbers=12×a12

We add a new number, x:

a13=(sumOf12Numbers+x)/13

13×a13=12×a12+x

x=13×a13-12×a12=13×5-12×3=65-36=29

The thirteenth number is 29

Answer 2

Answer: The thirteenth number is 29

Step-by-step explanation: We shall by looking at the available bits of information. We already have a mean of 12 positive numbers which is 3. The addition of the numbers divided by 12 would result in the mean. This we can express as follows;

Summation/12 = 3

That basically is the formula for calculating a set of data/numbers.

If we cross multiply, the expression becomes;

Summation = 3 x 12

Summation = 36.

That means if we add up all 12 positive numbers we would have 36. When another is added the mean becomes 5. That is,

(36 + a)/13 = 5

That means the summation is now 36 + a, and the observed data is now 13, while the mean is now 5. Therefore,

(36 + a)/13 = 5

We cross multiply and we have,

36 + a = 5 x 13

36 + a = 65

Subtract 36 from both sides of the equation

a = 29

Therefore the 13th number is 29.