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.
| | Year 1 | Year 2 | Year 3 |
| -------------------- | ------ | ------ | ------ |
| Zebra Swallowtail | 21 | 10 | 10 |
| Viceroy | 3 | 4 | 3 |
| Painted Lady | 2 | 0 | 16 |
| Monarch | 82 | 52 | 57 |
A. The average number of monarchs over all three samples is less than the number of monarchs counted in year 3.
B. The Viceroy population remained fairly steady over the three years recorded.
C. The average number of Zebra Swallowtails over all three samples will be less than the number recorded in year 1.
D. If a population is increasing over time, the average will be less than the most recent count.
E. There was a mistake in the sample for year 3 as the Painted Ladies were extinct in year?
Answer (2)
Based on the butterfly populations data, the correct inferences are that the Viceroy population was steady, the average number of Zebra Swallowtails is less than the count in year 1, and if a population increases, the average is lower than the most recent count. The incorrect statements are regarding the Monarchs and the assumption of mistakes in the Painted Lady counts. Thus, the chosen options are B, C, and D.
;
Calculate the average number of Monarchs: 3 82 + 52 + 57 ≈ 63.67 . Since 63.67 > 57, the first statement is false.
The Viceroy population remained fairly steady.
Calculate the average number of Zebra Swallowtails: 3 21 + 10 + 10 ≈ 13.67 . Since 13.67 < 21, the third statement is true.
If a population is increasing over time, the average will be less than the most recent count.
The three correct inferences are: The Viceroy population remained fairly steady, the average number of Zebra Swallowtails will be less than the number recorded in year 1, and if a population is increasing over time, the average will be less than the most recent count.
Explanation
Analyze the data Let's analyze the given data and statements to determine which inferences are valid. We have the butterfly counts for Zebra Swallowtail, Viceroy, Painted Lady, and Monarch butterflies over three years.
Analyze Monarch data First, let's check the statement about Monarchs. The average number of Monarchs over the three years is calculated as follows: 3 82 + 52 + 57 = 3 191 ≈ 63.67
The number of Monarchs counted in year 3 is 57. Since 63.67 is not less than 57, the statement 'The average number of monarchs over all three samples is less than the number of monarchs counted in year 3' is false.
Analyze Viceroy data Next, let's consider the Viceroy population. The counts are 3, 4, and 3 over the three years. These numbers are quite close to each other. So, the statement 'The Viceroy population remained fairly steady over the three years recorded' is true.
Analyze Zebra Swallowtail data Now, let's analyze the Zebra Swallowtail population. The average number of Zebra Swallowtails over the three years is calculated as follows: 3 21 + 10 + 10 = 3 41 ≈ 13.67 The number of Zebra Swallowtails recorded in year 1 is 21. Since 13.67 is less than 21, the statement 'The average number of Zebra Swallowtails over all three samples will be less than the number recorded in year 1' is true.
Analyze Painted Lady data Let's examine the Painted Lady population. The counts are 2, 0, and 16. The population decreased to 0 in year 2 and then increased to 16 in year 3. Therefore, the statement 'There was a mistake in the sample for year 3 as the Painted Ladies were extinct in year 2' is false, as the population rebounded in year 3.
Analyze increasing population statement Finally, let's consider the statement 'If a population is increasing over time, the average will be less than the most recent count.' For the Painted Lady butterfly, the population increased significantly from year 2 (0) to year 3 (16). The average number of Painted Ladies is (2+0+16)/3 = 6. Since 6 is less than 16, this statement holds true for the Painted Lady population. Therefore, the statement 'If a population is increasing over time, the average will be less than the most recent count' is true.
Final Answer Therefore, the three correct inferences are:
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.
Examples
Understanding butterfly population trends can help scientists assess the health of an ecosystem. For example, if a particular butterfly species is declining, it could indicate habitat loss or the effects of pesticides. By tracking these populations over time, conservation efforts can be targeted to protect these important pollinators.
