To calculate the 5-number summary (Minimum, Q1, Median, Q3, Maximum) for the given dataset, we follow these steps:

Step 1: Organize the Data

Here’s the dataset provided, sorted in ascending order: $2, 3, 8, 12, 13, 14, 17, 38, 46, 48, 52, 92, 94, 97, 100$

Step 2: Calculate the Five Number Summary

1. Minimum (Min): This is the smallest value in the dataset. $\text{Min} = 2$

2. First Quartile (Q1): This is the median of the lower half of the dataset (excluding the overall median if the dataset has an odd number of observations). The lower half consists of: $2, 3, 8, 12, 13, 14, 17$ The median of this lower half is the value in the middle: $Q1 = 12$

3. Median (Q2): This is the middle value of the dataset. Since we have 15 data points, the median is the 8th value: $\text{Median} = 38$

4. Third Quartile (Q3): This is the median of the upper half of the dataset (excluding the overall median if the dataset has an odd number of observations). The upper half consists of: $46, 48, 52, 92, 94, 97, 100$ The median of this upper half is: $Q3 = 92$

5. Maximum (Max): This is the largest value in the dataset. $\text{Max} = 100$

Final 5-number summary:

• Min: 2
• Q1: 12
• Median: 38
• Q3: 92
• Max: 100

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Would you like further details or have any questions?

Here are some related questions to expand on this:

1. How do you calculate quartiles for larger datasets?
2. Can you explain the interquartile range (IQR) and how it's used?
3. How does the five-number summary help in identifying outliers?
4. How would the five-number summary change if an additional data point was added?
5. What are the differences between the five-number summary and a box plot?

Tip: The interquartile range (IQR) is a useful measure of variability that is resistant to outliers, calculated as $IQR = Q3 - Q1$.