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Question 4 (Multiple Choice, Worth 2 points)

The table shows the length, in inches, of fish in a pond.
\begin{tabular}{|l|l|l|l|}
\hline 15 & 18 & 9 & 22 \\
\hline 7 & 15 & 10 & 18 \\
\hline
\end{tabular}

Determine if the data contains any outliers. If so, list the outliers.

A. There is an outlier at 22.
B. There is an outlier at 7.
C. There are outliers at 7 and 22.
D. There are no outliers.



Answer :

GinnyAnswer
Let's analyze the data step-by-step:

1. Fish lengths:
The given lengths of fish are: 15, 18, 9, 22, 7, 15, 10, and 18.

2. Find Q1 and Q3 (the first and third quartiles):
- To find Q1 (the 25th percentile), we need to arrange the data in ascending order:
7, 9, 10, 15, 15, 18, 18, 22
- Q1 is the median of the first half of the data (not including the median if the amount of data is odd):
For 7, 9, 10, 15 (first half): Q1 = 9.75
- Q3 is the median of the second half of the data:
For 15, 18, 18, 22 (second half): Q3 = 18.0

3. Calculate the Interquartile Range (IQR):
IQR = Q3 - Q1 = 18.0 - 9.75 = 8.25

4. Determine the lower bound and the upper bound for outliers:
- Lower bound = Q1 - 1.5 IQR = 9.75 - 1.5 8.25 = -2.625
- Upper bound = Q3 + 1.5 IQR = 18.0 + 1.5 8.25 = 30.375

5. Identify the outliers:
An outlier is a number that falls below the lower bound (-2.625) or above the upper bound (30.375).
- Here, none of the given fish lengths (7, 9, 10, 15, 15, 18, 18, 22) fall outside the range -2.625 to 30.375.

Therefore, there are no outliers.

### Conclusion:
The correct choice is:
- There are no outliers.

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