Yearly population increases for the last five years in a particular city were 2.48%, 1.11%, 3.86%, 2.36%, and 3.78%. Calculate the annual average increase in population. Give your answer as a percent accurate to at least **three** decimal places.


Average =0.00%


To find the annual average increase in population over the last five years, we need to calculate the arithmetic mean of the yearly percentage increases. The arithmetic mean is given by the formula:

\[
\text{Average} = \frac{\sum \text{Percentage Increases}}{\text{Number of Years}}
\]

Here are the steps to calculate it:

1. List the yearly percentage increases:
   \[
   2.48\%, 1.11\%, 3.86\%, 2.36\%, 3.78\%
   \]

2. Calculate the sum of these percentages:
   \[
   2.48 + 1.11 + 3.86 + 2.36 + 3.78 = 13.59
   \]

3. Divide the sum by the number of years (5):
   \[
   \text{Average} = \frac{13.59}{5} = 2.718
   \]

Therefore, the annual average increase in population, accurate to at least three decimal places, is \( \boxed{2.718\%} \).

Would you like more details or have any questions?

Here are some questions you might want to ask:
1. What is the arithmetic mean?
2. How do you sum the percentages correctly?
3. Why do we divide by the number of years to find the average?
4. What is the significance of calculating an average percentage increase?
5. Can you explain how to ensure accuracy when calculating percentages?

**Tip:** When averaging percentages, ensure that you use the arithmetic mean unless instructed otherwise, as it provides a straightforward measure of central tendency for the data set.

Learn how to calculate the annual average increase in population based on yearly percentage increases of 2.48%, 1.11%, 3.86%, 2.36%, and 3.78%. This problem involves arithmetic mean and percentage increase calculations, providing a detailed solution accurate to three decimal places. Suitable for students in Grades 9-12.

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