Let's break down the information from the image, which presents a box plot and several related questions:

The Box Plot Data:

• Minimum: 12
• Q1 (First Quartile): 14
• Median (Q2): 16.5
• Q3 (Third Quartile): 18
• Maximum: 23

Questions and Answers:

1. What is the range?

   • The range is the difference between the maximum and minimum values.
   • $\text{Range} = 23 - 12 = 11$

2. What is the interquartile range (IQR) of the data?

   • The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
   • $\text{IQR} = 18 - 14 = 4$

3. What does the 23 represent in the box?

   • The value 23 represents the maximum value in the data set, or the upper whisker in the box plot.

4. What percentage of the data is less than 14?

   • In a box plot, 25% of the data lies below the first quartile (Q1), which is 14.

5. What percentage of the data is between 14 and 18?

   • The data between the first quartile (Q1) and the third quartile (Q3) accounts for 50% of the data. Therefore, 50% of the data is between 14 and 18.

Would you like more details on any specific question or need further clarification?

Related Questions:

1. How would you find the median from a box plot if it wasn't labeled?
2. What does it mean if the IQR is small compared to the range?
3. How can you interpret outliers in a box plot?
4. If another data point is added above 23, how would that affect the range?
5. Why is the interquartile range useful compared to just using the range?

Tip:

The interquartile range (IQR) is more robust to outliers than the range since it focuses on the middle 50% of the data.