The mean of 14 numbers is 50. Removing one of the numbers causes the mean to decrease to 43. What number was removed?

14*50 - 13*43

Well, this sounds like a tricky math problem, but don't worry, I'm here to make it fun! Let's see, the mean of the 14 numbers is 50, right? So, the total sum of all those numbers would be 14 multiplied by 50, which is 700.

Now, when we remove one of the numbers, the mean decreases to 43. That means the new total sum of the remaining 13 numbers would be 13 multiplied by 43, which is 559.

To find out which number was removed, we need to calculate the difference between the original sum (700) and the new sum (559). And guess what? That difference is the mysterious missing number!

So, 700 minus 559 is 141. Ta-da! The number that was removed is 141. I hope I didn't clown around too much with the math!

To solve this problem, we can use the formula for the mean:

Mean = Sum of numbers / Number of numbers

Given that the mean of the 14 numbers is 50, we can set up the equation:

50 = (Sum of 14 numbers) / 14

Multiplying both sides of the equation by 14, we get:

Sum of 14 numbers = 50*14 = 700

Now, let's assume that the number to be removed is "x". Without this number, the mean decreases to 43. So, we can set up another equation:

43 = (Sum of 14 numbers - x) / (14 - 1)

or

43 = (700 - x) / 13

Multiplying both sides of the equation by 13, we get:

13*43 = 700 - x

Simplifying the equation, we have:

559 = 700 - x

Rearranging the equation, we get:

x = 700 - 559 = 141

Therefore, the number that was removed is 141.

To find the number that was removed, we need to first understand how the mean is calculated.

The mean of a set of numbers is found by adding up all the numbers in the set and then dividing the sum by the total number of values in the set.

Let's say the 14 numbers are represented as x₁, x₂, x₃, ..., x₁₄.

We know that the mean of these 14 numbers is 50. So, we can write the equation as:

(x₁ + x₂ + x₃ + ... + x₁₄) / 14 = 50

Next, we are given that removing one of the numbers causes the mean to decrease to 43. If we remove a number, we are left with only 13 numbers. Let's assume the number removed is xᵢ, where i is the position of the removed number.

The new equation becomes:

((x₁ + x₂ + x₃ + ... + x₁₄) - xᵢ) / 13 = 43

Now, we have two equations with two unknowns (x₁₄ and xᵢ) but we can solve this system of equations to find the value of xᵢ.

Simplifying the equations, we get:

(x₁ + x₂ + x₃ + ... + x₁₄) = 14 * 50

(x₁ + x₂ + x₃ + ... + x₁₃) - xᵢ = 13 * 43

Let's subtract the second equation from the first equation to eliminate xᵢ:

(x₁ + x₂ + x₃ + ... + x₁₄) - ((x₁ + x₂ + x₃ + ... + x₁₃) - xᵢ) = (14 * 50) - (13 * 43)

Simplifying further:

xᵢ = (14 * 50) - (13 * 43) + x₁₃

So, to find the number that was removed, you would need to compute the right side of this equation.