To answer the question, we need to analyze the data in the table to identify any clusters or outliers among the values. Here is a step-by-step analysis:
1. Identify the given data:
- [tex]\( x \)[/tex] values: [2.1, 2.5, 2.7, 3.1, 3.4, 3.9, 4.2]
- [tex]\( y \)[/tex] values: [30, 36, 34, 38, 39, 42, 41]
2. Calculate the mean ([tex]\(\mu\)[/tex]) and standard deviation ([tex]\(\sigma\)[/tex]) of [tex]\( y \)[/tex] values:
- Mean ([tex]\( \mu \)[/tex]) of [tex]\( y \)[/tex] = 37.142857142857146
- Standard deviation ([tex]\( \sigma \)[/tex]) of [tex]\( y \)[/tex] = 3.8702687663983054
3. Determine the bounds to identify outliers:
- Lower bound = Mean - 2 Standard deviation = 29.402161609060535
- Upper bound = Mean + 2 Standard deviation = 44.88355267665376
4. Identify outliers:
- An outlier is any value outside the range [29.402161609060535, 44.88355267665376].
- Checking our [tex]\( y \)[/tex] values:
- 30, 36, 34, 38, 39, 42, and 41 are all within the range [29.402161609060535, 44.88355267665376].
- Therefore, there are no outliers.
5. Identify clusters:
- A cluster can be identified by looking at values that are close to each other within the acceptable range.
- The [tex]\( y \)[/tex] values [30, 36, 34, 38, 39, 42, 41] suggest they are closely grouped together within the range, indicating there is a cluster.
6. Conclusion:
- Since there are no outliers and there is a cluster, the most accurate description of the data is:
- There are no outliers, but there is a cluster.
Thus, the best description of the data in the table is:
- There are no outliers, but there is a cluster.
