Let's break down the boxplot and solve the questions based on the information provided:

From the boxplot:

• Minimum value = 17
• First quartile (Q1) = 30
• Median (Q2) = 46
• Third quartile (Q3) = 57
• Maximum value = 75

Answers:

a. What quarter has the smallest spread of data?

• The second quarter (Q2) refers to the range between the first quartile (30) and the median (46).
• The third quarter refers to the range between the median (46) and the third quartile (57).
• The fourth quarter refers to the range between the third quartile (57) and the maximum (75).

From the boxplot, we see that the third quarter (46 to 57) has the smallest spread.

• Answer: Third Quarter.

b. What is that spread?

• The spread of the third quarter is the difference between Q3 and the median.

• $57 - 46 = 11$.

• Answer: 11.

c. Find the Interquartile Range (IQR):

• The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

• $57 - 30 = 27$.

• Answer: IQR = 27.

d. Which interval has the most data in it?

• The interval that contains the median (Q2) typically has the most data.

• This is between 30 and 46, which is the second quarter.

• Answer: 30 - 46.

e. What value could represent the 79th percentile?

• The 79th percentile would be in the fourth quarter, as it is higher than the third quartile (75th percentile).

• The fourth quarter ranges from 57 to 75.

• Among the given options, 60 is the closest value to represent the 79th percentile.

• Answer: 60.

Do you want more details on any of these answers? Here are 5 related questions to consider:

1. What is the significance of the Interquartile Range (IQR) in data analysis?
2. How can you use a boxplot to identify potential outliers?
3. What does the median represent in a dataset, and why is it important?
4. How would you calculate the percentile rank for other values in the dataset?
5. What are some limitations of using boxplots for analyzing data distribution?

Tip: In any dataset, the Interquartile Range (IQR) helps identify the middle 50% of the data and is useful for spotting potential outliers when combined with the lower and upper bounds.