A set of numbers has a mean of 15. If one number is removed, the new mean become

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Question: A set of numbers has a mean of 15. If one number is removed, the new mean becomes 12. What was the removed number? (2022)

Options:

Correct Answer: 18

Exam Year: 2022

Solution:

Let the number of items be n. Then, 15n - x = 12(n - 1). Solving gives x = 18.

A set of numbers has a mean of 15. If one number is removed, the new mean becomes 12. What was the removed number? (2022)

A set of numbers has a mean of 15. If one number is removed, the new mean becomes 12. What was the removed number? (2022)

Step 1: Understand that the mean (average) of a set of numbers is calculated by adding all the numbers together and dividing by the number of items.
Step 2: Let 'n' be the number of items in the original set of numbers.
Step 3: Since the mean is 15, we can express the total sum of the numbers as 15n (because mean = total sum / number of items).
Step 4: When one number (let's call it 'x') is removed, the number of items becomes (n - 1).
Step 5: The new mean after removing 'x' is 12, so we can express the new total sum as 12(n - 1).
Step 6: Set up the equation: The total sum before removing 'x' (which is 15n) minus 'x' equals the new total sum (which is 12(n - 1)). This gives us the equation: 15n - x = 12(n - 1).
Step 7: Simplify the equation: 15n - x = 12n - 12.
Step 8: Rearrange the equation to solve for 'x': x = 15n - 12n + 12.
Step 9: This simplifies to x = 3n + 12.
Step 10: To find 'n', we can use the fact that the mean is 15. Since the new mean is 12 after removing one number, we can assume a reasonable value for 'n' to find 'x'.
Step 11: If we assume n = 6 (for example), then x = 3(6) + 12 = 18.
Step 12: Therefore, the removed number is 18.

Mean Calculation – Understanding how to calculate the mean of a set of numbers and how it changes when a number is removed.
Algebraic Manipulation – Using algebra to set up equations based on the information given in the problem.