Question

the table displays the number of butterflies collected in a sample over three years. what inferences can be made from the samples taken on butterfly populations? select three choices. louden county butterfly count year 1 year 2 year 3 zebra swallowtail 21 zebra swallowtail 10 zebra swallowtail 10 viceroy 3 viceroy 4 viceroy 3 painted lady 2 painted lady 0 painted lady 16 monarch 82 monarch 52 monarch 57 the average number of monarchs over all three samples is less than the number of monarchs counted in year 3. the viceroy population remained fairly steady over the three years recorded. the average number of zebra swallowtails over all three samples will be less than the number recorded in year 1. if a population is increasing over time, the average will be less than the most recent count. there was a mistake in the sample for year 3 as the painted ladies were extinct in year 2.

Explanation:

Step1: Calculate average of Monarchs

Average = $\frac{82 + 52+57}{3}=\frac{191}{3}\approx63.67$. Since $63.67>57$, the first statement is false.

Step2: Analyze Viceroy population

Viceroy counts are 3, 4, 3. The values are close, so the population remained fairly steady.

Step3: Calculate average of Zebra Swallowtails

Average = $\frac{21 + 10+10}{3}=\frac{41}{3}\approx13.67$. Since $13.67<21$, the average number of Zebra - Swallowtails over all three samples is less than the number recorded in year 1.

Step4: Consider population increase and average

If a population is increasing over time, earlier lower counts will pull the average down, so the average will be less than the most recent count.

Step5: Analyze Painted Lady situation

Just because Painted Ladies were 0 in year 2 doesn't mean they were extinct, and there's no evidence of a mistake in year 3 sample.

Answer:

The Viceroy population remained fairly steady over the three years recorded.
The average number of Zebra Swallowtails over all three samples will be less than the number recorded in year 1.
If a population is increasing over time, the average will be less than the most recent count.