explain why the average change from the start of a period to the end is also zero?

To explain why the average change from the start of a period to the end is also zero, we need to understand what average means and how changes are measured.

Average represents the central tendency of a set of numbers. It is found by summing up all the values in a data set and dividing it by the number of values. In this case, we are considering the average change.

Change, on the other hand, refers to the difference between two values. It is calculated by subtracting the initial value from the final value.

Now, let's consider a period where we have a starting value and an ending value. The change from the start to the end can be positive, negative, or zero, depending on the values.

If the change is positive, it means the ending value is greater than the starting value. If the change is negative, it means the ending value is smaller than the starting value. And if the change is zero, it means the ending value is the same as the starting value.

In a given period, there will be cases where the change is positive, cases where it is negative, and cases where it is zero. When we calculate the average change for the entire period, we consider all these changes.

Now, let's analyze why the average change from the start of a period to the end is zero. To get this result, we need to consider the changes individually and their impact on the average.

If there is a positive change in value, it contributes a positive value to the average, indicating an increase. If there is a negative change in value, it contributes a negative value to the average, indicating a decrease. And if there is a zero change in value, it contributes zero to the average.

Since we are considering the average change for the entire period, with all the positive, negative, and zero changes, these contributions balance each other out. For every positive change, there will be a corresponding negative change, and for every nonzero change, there will be a zero change. As a result, the net effect is zero.

Therefore, the average change from the start of a period to the end is also zero because the positive and negative changes cancel each other out when summed and divided by the total number of changes.