Question

select the button to take a sample of fish. sometimes populations change over time. generate six samples for one year after the initial samples. identify the ratio of the average number of bass to the average number of fish in the sample.
fish type s1 s2 s3 s4 s5 s6
brook trout 8 12 6 5 9 10
catfish 6 7 9 7 8 9
smallmouth bass 6 1 5 8 3 1
o 1:5
o 1:4
o 3:10
o 9:20

Explanation:

Step1: Calculate average number of bass

First, find the sum of bass in all samples: $6 + 1+5 + 8+3 + 1=24$. Then, divide by the number of samples ($n = 6$). The average number of bass $\bar{x}_{bass}=\frac{24}{6}=4$.

Step2: Calculate average number of total fish

For each sample, find the total number of fish:
Sample 1: $8 + 6+6=20$; Sample 2: $12 + 7+1 = 20$; Sample 3: $6+9 + 5=20$; Sample 4: $5+7 + 8=20$; Sample 5: $9+8 + 3=20$; Sample 6: $10+9 + 1=20$.
The sum of total - fish in all samples is $20\times6 = 120$. The average number of fish per sample $\bar{x}_{fish}=\frac{120}{6}=20$.

Step3: Find the ratio

The ratio of the average number of bass to the average number of fish is $\frac{\bar{x}_{bass}}{\bar{x}_{fish}}=\frac{4}{20}=\frac{1}{5}$, or $1:5$.

Answer:

1:5