Revising the Average: Correcting a Calculation Error

In many scenarios, the accuracy of calculated averages is crucial. This article explores a common error in the calculation of an average and demonstrates how to rectify this mistake.

Suppose the average of ten numbers is initially calculated as 16. After thorough review, it is discovered that the number 55 was incorrectly read as 25.

The Role of the Incorrect Number

The incorrect number, 25, was used to compute the average, which led to a miscalculation. In reality, 55 should have been the correct value. To correct the error, you need to reassess the sum of the numbers involved.

Step 1: Calculate the Incorrect Sum

The initial average was calculated as follows:

Let the sum of the ten numbers be ( S ).

(frac{S}{10} 16)

(S 160)

However, the incorrect number 25 was used instead of the correct number 55 in the calculation. The difference between these two numbers is:

55 - 25 30

Step 2: Calculate the Correct Sum

To find the correct average, you must adjust the sum by subtracting the error. Therefore, the correct sum is:

Correct Sum 160 - 30 130

Step 3: Calculate the Correct Average

The correct average is then calculated by dividing the correct sum by the number of values:

(frac{130}{10} 13)

This shows that the initial average of 16 was incorrect due to the reading of 25 as 55. The correct average is 13.

Additional Examples

To further clarify, let's revisit a few similar cases:

Example 1:

Wrong Average of 10 numbers 15

Total sum of 10 numbers:

(15 times 10 150)

Since 55 was read as 25, the wrong sum is actually less by 30. The correct sum is:

150 30 180

Correct Average: (frac{180}{10} 18)

Example 2:

Average of 10 numbers 15