The five-number summary consists of the following key values from a data set: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Let's find these values for the given data set:

Data:

12, 18, 19, 32, 42, 48, 50, 64, 67, 76, 80, 82, 85, 96, 98

1. Minimum: The smallest number in the data set.

$\text{Minimum} = 12$

2. Maximum: The largest number in the data set.

$\text{Maximum} = 98$

3. Median (Q2): The middle value in the ordered data set.

There are 15 numbers, so the median is the 8th value. $\text{Median} = 64$

4. First Quartile (Q1): The median of the lower half of the data set (excluding the median).

The lower half of the data is: 12, 18, 19, 32, 42, 48, 50 The median of these values (7 numbers) is the 4th value. $\text{Q1} = 32$

5. Third Quartile (Q3): The median of the upper half of the data set (excluding the median).

The upper half of the data is: 67, 76, 80, 82, 85, 96, 98 The median of these values (7 numbers) is the 4th value. $\text{Q3} = 82$

Five-number summary:

$\boxed{12, 32, 64, 82, 98}$

Would you like more details or further explanation on any of these steps?

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Here are some related questions to expand on this topic:

1. How is the interquartile range (IQR) calculated from the five-number summary?
2. What is the difference between a five-number summary and a box plot?
3. How would outliers be identified using the five-number summary?
4. Can the five-number summary be used for non-numerical data sets?
5. What are the advantages of using the five-number summary in data analysis?

Tip: The interquartile range (IQR) is often used to detect outliers, as any data point below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$ is typically considered an outlier.