To identify the 5-number summary for the given data set, we'll follow these steps:

Step 1: List all the values in ascending order

The given data is:

$32, 6, 26, 60, 80, 36, 29, 100, 74, 21, 99, 67, 24, 43, 66, 58, 89, 90, 38, 10, 59, 75, 69, 86$

Arranging these values in ascending order:

$6, 10, 21, 24, 26, 29, 32, 36, 38, 43, 58, 59, 60, 66, 67, 69, 74, 75, 80, 86, 89, 90, 99, 100$

Step 2: Calculate the 5-number summary

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

   • $\text{Min} = 6$

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

   • $\text{Max} = 100$

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

   • Since there are 24 values, the median will be the average of the 12th and 13th values:
   • Median $Q2 = \frac{59 + 60}{2} = 59.5$

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

   • The lower half includes the first 12 values: $6, 10, 21, 24, 26, 29, 32, 36, 38, 43, 58, 59$
   • $Q1 = \frac{29 + 32}{2} = 30.5$

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

   • The upper half includes the last 12 values: $60, 66, 67, 69, 74, 75, 80, 86, 89, 90, 99, 100$
   • $Q3 = \frac{75 + 80}{2} = 77.5$

Final 5-number summary:

• Minimum: 6
• First Quartile (Q1): 30.5
• Median (Q2): 59.5
• Third Quartile (Q3): 77.5
• Maximum: 100

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:

1. How does the mean compare to the median in this data set?
2. What does the interquartile range (IQR) tell you about the spread of the middle 50% of data?
3. How would the 5-number summary change if an outlier was added to this data set?
4. Can you identify any potential outliers in this data set?
5. How does the 5-number summary help in constructing a box plot?

Tip: Always ensure that data is sorted correctly before calculating the quartiles for an accurate 5-number summary.