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Determining a Sample Error

Paris used a simulation to take two random samples of fish in a pond. Her sample size was 30, and the table shows the frequency of each fish in the sample. Paris used the two samples to predict that the average number of trout will be 6, the average number of catfish will be 5, and the average number of bass will be 18.

\begin{tabular}{|c|c|c|}
\hline
Fish Type & \begin{tabular}{c}
Frequency \\
Sample 1
\end{tabular} & \begin{tabular}{c}
Frequency \\
Sample 2
\end{tabular} \\
\hline
Brook Trout & 12 & 1 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the sample error for the prediction regarding the Brook Trout, we need to follow these steps:

1. Understand the Given Data:
- Predicted numbers based on the samples:
- Average number of trout: 6
- Average number of catfish: 5
- Average number of bass: 18

- Frequencies from the samples for Brook Trout:
- Sample 1: 12 Brook Trout
- Sample 2: 1 Brook Trout

2. Calculate the Mean Number of Brook Trout:
- We have two samples and the frequencies of Brook Trout in these samples. To find the average (mean) number of Brook Trout in these samples, we add up the frequencies of Brook Trout from both samples and divide by the number of samples.

[tex]\[ \text{Mean Brook Trout} = \frac{\text{Frequency in Sample 1} + \text{Frequency in Sample 2}}{2} \][/tex]

Substituting in the frequencies:

[tex]\[ \text{Mean Brook Trout} = \frac{12 + 1}{2} \][/tex]

3. Perform the Calculation:

[tex]\[ \text{Mean Brook Trout} = \frac{12 + 1}{2} = \frac{13}{2} = 6.5 \][/tex]

4. Result:
- After performing these calculations, we find that the mean number of Brook Trout based on the two samples is 6.5.

This detailed step-by-step solution outlines how we determine the average number of Brook Trout from the two samples provided and find that it is 6.5.

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