If the average of 12 numbers is 25, what is the average if one number is replace

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Question: If the average of 12 numbers is 25, what is the average if one number is replaced by 35?

Options:

Correct Answer: 26

Solution:

Total = 12 * 25 = 300. New total = 300 - x + 35. New average = (300 - x + 35) / 12.

If the average of 12 numbers is 25, what is the average if one number is replaced by 35?

If the average of 12 numbers is 25, what is the average if one number is replaced by 35?

Step 1: Understand that the average of 12 numbers is 25.
Step 2: Calculate the total of these 12 numbers by multiplying the average by the number of numbers: 12 * 25 = 300.
Step 3: Identify that one of the 12 numbers (let's call it 'x') will be replaced by 35.
Step 4: Calculate the new total after replacing 'x' with 35: New total = 300 - x + 35.
Step 5: Simplify the new total: New total = 300 - x + 35 = 335 - x.
Step 6: To find the new average, divide the new total by the number of numbers (which is still 12): New average = (335 - x) / 12.
Step 7: Note that we cannot find the exact new average without knowing the value of 'x', but we have the formula for it.

Average Calculation – Understanding how to calculate the average of a set of numbers and how it changes when one number is replaced.
Total Sum of Numbers – Calculating the total sum of numbers from the average and the number of elements.
Impact of Replacement – Analyzing how replacing a number affects the overall average.