To determine whether each value in the dataset is an outlier or not, we use the Interquartile Range (IQR), which helps us identify the range within which most of the data points lie. Here's the step-by-step process:
1. Find the 1st Quartile (Q1) and the 3rd Quartile (Q3):
[tex]\[
Q1 = 3.9, \quad Q3 = 6.45
\][/tex]
2. Calculate the Interquartile Range (IQR):
[tex]\[
IQR = Q3 - Q1 = 6.45 - 3.9 = 2.55
\][/tex]
3. Determine the lower and upper bounds for outliers:
[tex]\[
\text{Lower bound} = Q1 - 1.5 \times IQR = 3.9 - 1.5 \times 2.55 = 0.075
\][/tex]
[tex]\[
\text{Upper bound} = Q3 + 1.5 \times IQR = 6.45 + 1.5 \times 2.55 = 10.275
\][/tex]
4. Identify the outliers based on these bounds:
- A value is considered an outlier if it is less than the lower bound (0.075) or greater than the upper bound (10.275).
Now, let's classify each data point:
- 0.8:
[tex]\[
0.075 \leq 0.8 \leq 10.275 \rightarrow \text{Not Outlier}
\][/tex]
- 1.6:
[tex]\[
0.075 \leq 1.6 \leq 10.275 \rightarrow \text{Not Outlier}
\][/tex]
- 10.6:
[tex]\[
10.6 > 10.275 \rightarrow \text{Outlier}
\][/tex]
- 11.2:
[tex]\[
11.2 > 10.275 \rightarrow \text{Outlier}
\][/tex]
Thus, the final results are:
\begin{tabular}{|c|c|c|}
\hline
Data & Outlier & Not Outlier \\
\hline
0.8 & & ✓ \\
\hline
1.6 & & ✓ \\
\hline
10.6 & ✓ & \\
\hline
11.2 & ✓ & \\
\hline
\end{tabular}
