In some scenarios, you may need to exclude certain data points from your calculations to find a more accurate or relevant average. This process is known as 'excluding data points.'
In the given problem, we are asked to exclude the highest and lowest scores from the dataset. Let's understand this concept with the steps already provided:
- First, determine the sum of the entire dataset using the given average formula.
- Next, identify the values you need to exclude. Here, they are the highest and lowest scores.
- Subtract these values from the total sum.
From the solution, we know: and
So, the sum of the remaining scores after excluding the highest and lowest is: .
To find the new average, divide this sum by , the adjusted number of data points. The formula is:
This process ensures that our new average accurately reflects the remaining data by fairly distributing the sum over the adjusted number of students.