Let's first break down the task based on the data provided:

The scores of 13 students in ascending order are:

$63, 64, 70, 76, 80, 80, 82, 84, 87, 91, 92, 94$

Step 1: Five-number summary

The five-number summary consists of:

1. Minimum: The smallest number in the dataset.
2. Lower Quartile (Q1): The 25th percentile, which is the median of the lower half of the data.
3. Median (Q2): The middle number in the dataset.
4. Upper Quartile (Q3): The 75th percentile, which is the median of the upper half of the data.
5. Maximum: The largest number in the dataset.

Minimum and Maximum

• Minimum: 63
• Maximum: 94

Median (Q2)

The dataset has 13 numbers, so the median is the 7th number.

• Median: 82

Lower Quartile (Q1)

The lower half of the data (excluding the median) is: $63, 64, 70, 76, 80, 80$ The median of this subset is the average of the 3rd and 4th numbers: $Q1 = \frac{70 + 76}{2} = 73$

Upper Quartile (Q3)

The upper half of the data (excluding the median) is: $84, 87, 91, 92, 94$ The median of this subset is the 3rd number: $Q3 = 87$

Step 2: Interquartile Range (IQR)

The interquartile range is given by: $IQR = Q3 - Q1 = 87 - 73 = 14$

Final Results:

• Minimum: 63
• Lower Quartile (Q1): 73
• Median (Q2): 82
• Upper Quartile (Q3): 87
• Maximum: 94
• Interquartile Range (IQR): 14

Would you like more details on any of these calculations?

Here are 5 related questions to expand on this:

1. How is the interquartile range useful in statistics?
2. What do outliers look like using the five-number summary and IQR?
3. How would you create a box plot using this five-number summary?
4. What other methods could be used to describe the spread of data?
5. How does the size of the IQR compare to the overall range of this dataset?

Tip: The interquartile range (IQR) helps you understand the spread of the middle 50% of your data. It's useful for identifying outliers!