8 ,9 ,10 ,11 ,12 ,13 ,14 ,15 ,16 ,17 ,18 ,19  


For the data this box plot is based on, 
% of the data values are between 8 and 9.

Also, 
% of the data values are between 9 and 14, 
% of the data values are between 14 and 18, and 
% of the data values are between 18 and 19.

A box plot divides the data into quartiles, meaning it separates the data into four equal parts. Here’s how to determine the percentages based on the given values:

1. **Data Range and Quartiles**:  
   The values provided are: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. Since these are equally spaced and form a sequence of 12 data points, we'll split them into quartiles:

   - **Q1 (First Quartile)**: This is the 25th percentile of the data.
   - **Q2 (Median)**: This is the 50th percentile (median) of the data.
   - **Q3 (Third Quartile)**: This is the 75th percentile of the data.

2. **Calculating Percentages**:

   - **% of the data values between 8 and 9**:  
     Since the data points are evenly spaced, and the values 8 and 9 represent only the first two points in the sequence (out of 12 total), this range includes \(\frac{2}{12} \times 100 = 16.67\%\).

   - **% of the data values between 9 and 14**:  
     The values 9 through 14 include the 2nd to 6th data points. This range represents 5 points, so \(\frac{5}{12} \times 100 \approx 41.67\%\).

   - **% of the data values between 14 and 18**:  
     The values 14 through 18 include the 6th to 10th data points. This range also includes 5 points, which again corresponds to approximately \(41.67\%\).

   - **% of the data values between 18 and 19**:  
     The values 18 and 19 are the last two data points (out of 12), so this range accounts for \(\frac{2}{12} \times 100 = 16.67\%\).

### Summary:
1. **Between 8 and 9**: 16.67%
2. **Between 9 and 14**: 41.67%
3. **Between 14 and 18**: 41.67%
4. **Between 18 and 19**: 16.67%

Would you like more details or have any questions?

### Questions:
1. What are the quartile values (Q1, median, and Q3) for this data set?
2. How is the interquartile range (IQR) calculated and what does it represent?
3. What percentage of data lies between the 1st and 3rd quartile (Q1 and Q3)?
4. How can you identify outliers using a box plot?
5. What is the range and how is it different from the interquartile range?

### Tip:
To find the quartiles accurately, always arrange the data in ascending order and divide it into equal parts.

For the data this box plot is based on, what percentage of the data values are between 8 and 9, between 9 and 14, between 14 and 18, and between 18 and 19?

This problem explores how to calculate the percentage of data values between specified ranges in a box plot. Understand how quartiles work and how to use them to calculate percentages for ranges like 8-9, 9-14, 14-18, and 18-19. Ideal for students in Grades 6-8.

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