Question

1. the table shows the size of the deer population in a national park from 2016 to 2021. determine the average (mean) change per year in the size of the deer population.

year 2016 2017 2018 2019 2020 2021
number of deer 53 47 44 51 50 43
what does the sign of the mean change per year tell you about the deer population overall?

Explanation:

Step1: Calculate annual changes

First, find the change in population for each year:

• 2017: \(47 - 53 = -6\)
• 2018: \(44 - 47 = -3\)
• 2019: \(51 - 44 = 7\)
• 2020: \(50 - 51 = -1\)
• 2021: \(43 - 50 = -7\)

Step2: Sum the changes

Sum these annual changes: \(-6 + (-3) + 7 + (-1) + (-7) = -6 - 3 + 7 - 1 - 7 = -10\)

Step3: Calculate mean change

Number of years between 2016 - 2021 is \(2021 - 2016 = 5\) years (since we have 5 intervals).
Mean change per year: \(\frac{-10}{5} = -2\)

Answer:

The average (mean) change per year is \(-2\). The negative sign tells us that the deer population is decreasing overall (on average, the population decreases by 2 deer per year).