Given the 5-number summary of final grades:

60, 75, 88, 93, 100

select all that applies 

Question 9 options:

yes there is at least 1 outlier


right skewed


symmetric


left skewed


No outliers

Given the 5-number summary of final grades:

- Minimum: 60
- Q1 (1st Quartile): 75
- Median (Q2): 88
- Q3 (3rd Quartile): 93
- Maximum: 100

### To assess the possible distribution and outliers:

1. **Symmetry or Skewness**:
   - The gap between the median (88) and the lower quartile (75) is 13, while the gap between the median (88) and the upper quartile (93) is only 5. This indicates a **longer tail on the lower end** (towards lower values), suggesting that the distribution is **left-skewed**.

2. **Outliers**:
   - An outlier can be identified using the **interquartile range (IQR)** method. 
   - \( IQR = Q3 - Q1 = 93 - 75 = 18 \)
   - Any values outside the range \([Q1 - 1.5 \times IQR, Q3 + 1.5 \times IQR]\) may be considered outliers.
   - Lower bound = \( 75 - 1.5 \times 18 = 48 \)
   - Upper bound = \( 93 + 1.5 \times 18 = 120 \)
   - Since all values in the summary (60, 75, 88, 93, 100) fall within the range [48, 120], there are **no outliers**.

### Conclusion:
- **Left skewed**: Yes
- **No outliers**: Yes

### Therefore, the correct options are:
- **Left skewed**
- **No outliers**

Would you like more details or further explanations?

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Here are 5 questions to expand your knowledge:

1. How do you calculate the interquartile range (IQR)?
2. What are the steps to determine if a distribution is skewed?
3. How does the 5-number summary help in understanding a dataset?
4. What is the impact of skewness on the mean and median of a distribution?
5. How can outliers affect statistical measures like mean and variance?

**Tip**: Always visualize your data when possible (like using box plots) to easily spot outliers and skewness.

Given the 5-number summary of final grades: 60, 75, 88, 93, 100, select all that apply. Options: yes there is at least 1 outlier, right skewed, symmetric, left skewed, No outliers

Learn how to analyze a 5-number summary of final grades (60, 75, 88, 93, 100) to determine the skewness and whether there are any outliers. This problem uses the interquartile range (IQR) rule and highlights key concepts in descriptive statistics. Suitable for students in Grades 9-12.

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