The mean of five numbers is 20. If one number is removed, the mean of the remain

The mean of five numbers is 20. If one number is removed, the mean of the remaining numbers becomes 18. What is the number that was removed?

The mean of five numbers is 20. If one number is removed, the mean of the remaining numbers becomes 18. What is the number that was removed?

Step 1: Understand that the mean (average) of five numbers is 20.
Step 2: Use the formula for mean: Mean = Sum of numbers / Number of numbers.
Step 3: Since the mean is 20 for five numbers, we can write: Sum of five numbers (S) / 5 = 20.
Step 4: Multiply both sides by 5 to find the sum: S = 20 * 5 = 100.
Step 5: Now, one number is removed, and we need to find that number. Let's call the removed number 'x'.
Step 6: The new sum of the remaining four numbers is: S - x = 100 - x.
Step 7: The mean of the remaining four numbers is given as 18.
Step 8: Use the mean formula again for the four numbers: (New sum) / 4 = 18.
Step 9: Substitute the new sum into the formula: (100 - x) / 4 = 18.
Step 10: Multiply both sides by 4 to eliminate the fraction: 100 - x = 18 * 4.
Step 11: Calculate 18 * 4 = 72, so now we have: 100 - x = 72.
Step 12: Solve for x by subtracting 72 from 100: x = 100 - 72.
Step 13: Calculate the result: x = 28.

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