To find the 5-number summary for the data given, let’s go through each component. The 5-number summary consists of:

1. Minimum: The smallest value in the data set.
2. Q1 (First Quartile): The median of the lower half of the data (25th percentile).
3. Median (Q2): The middle value of the data set (50th percentile).
4. Q3 (Third Quartile): The median of the upper half of the data (75th percentile).
5. Maximum: The largest value in the data set.

The provided data, in ascending order, is: $4, 11, 14, 17, 27, 46, 47, 51, 55, 80, 83, 85, 93, 98$

Step-by-Step Solution:

1. Minimum: $4$
2. Maximum: $98$

To find the quartiles, we’ll use the following steps:

• Median (Q2): Since there are 14 values, the median will be the average of the 7th and 8th values. $\text{Median (Q2)} = \frac{47 + 51}{2} = 49$

• First Quartile (Q1): The first quartile is the median of the lower half (first seven values: $4, 11, 14, 17, 27, 46, 47$). $Q1 = 17$

• Third Quartile (Q3): The third quartile is the median of the upper half (last seven values: $51, 55, 80, 83, 85, 93, 98$). $Q3 = 83$

Final 5-Number Summary:

• Minimum: $4$
• Q1: $17$
• Median (Q2): $49$
• Q3: $83$
• Maximum: $98$

So, the correct answers should be: $4, 17, 49, 83, 98$

Let me know if you’d like more details on any of these steps!

Here are some related questions that might deepen your understanding:

1. How do you find quartiles for an odd number of data points?
2. What is the interquartile range, and how is it calculated?
3. How do outliers affect the five-number summary?
4. How can you use a boxplot to represent the five-number summary visually?
5. What is the difference between quartiles and percentiles?

Tip: Always arrange your data in ascending order before finding the five-number summary.