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Five geographical areas each have a total of 150 organisms distributed among four species: A, B, C, and D. Which area exhibits the highest evenness in the sample size?

\begin{tabular}{|c|l|}
\hline Name of the Area & Species Distribution \\
\hline Area 1 & [tex]$62 A , 37 B , 27 C , 4 D$[/tex] \\
\hline Area 2 & [tex]$80 A , 20 B , 8 C , 30 D$[/tex] \\
\hline Area 3 & [tex]$90 A , 40 B , 30 C , 15 D$[/tex] \\
\hline Area 4 & [tex]$38 A , 37 B , 37 C , 38 D$[/tex] \\
\hline Area 5 & [tex]$79 A , 12 B , 18 C , 41 D$[/tex] \\
\hline
\end{tabular}

A. Area 1
B. Area 2
C. Area 3
D. Area 4
E. Area 5



Answer :

GinnyAnswer
Let's evaluate the evenness of the species distribution for each area. Evenness measures how evenly organisms are distributed among the species in an area. Higher evenness means the distribution among species is more balanced.

1. Area 1:
- Species Distribution: 62 A, 37 B, 27 C, 4 D
- Total organisms: [tex]\(62 + 37 + 27 + 4 = 130\)[/tex]
- Let's check the evenness by examining how close each species count is to the mean count.

2. Area 2:
- Species Distribution: 80 A, 20 B, 8 C, 30 D
- Total organisms: [tex]\(80 + 20 + 8 + 30 = 138\)[/tex]
- Check the evenness by seeing the deviation from the mean count.

3. Area 3:
- Species Distribution: 90 A, 40 B, 30 C, 15 D
- Total organisms: [tex]\(90 + 40 + 30 + 15 = 175\)[/tex]
- Again, analyze the balance by comparing with the mean count.

4. Area 4:
- Species Distribution: 38 A, 37 B, 37 C, 38 D
- Total organisms: [tex]\(38 + 37 + 37 + 38 = 150\)[/tex]
- Given the distribution, it appears more even compared to others, meaning the counts for each species are very close to each other.

5. Area 5:
- Species Distribution: 79 A, 12 B, 18 C, 41 D
- Total organisms: [tex]\(79 + 12 + 18 + 41 = 150\)[/tex]
- Examine this for deviation from the mean.

From the above analysis:
- Area 4: Has a very balanced distribution where the counts of each species (38, 37, 37, 38) are almost identical, indicating high evenness.

Thus, among the given areas, Area 4 exhibits the highest evenness in the sample size.

The correct answer is D. Area 4.

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