The following are the distances (in miles) to the nearest airport for 12  families.
9,10,12,18,20,20,27,28,29,29,35,36
Notice that the numbers are ordered from least to greatest.

Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:	
 
Lower quartile:	
Median:	
Upper quartile:	
Maximum:	
Interquartile range


### Five-number summary:

1. **Minimum**: The smallest value in the dataset is **9**.

2. **Lower quartile (Q1)**: The lower quartile is the median of the lower half of the data (excluding the overall median). The lower half of the data set is:
   \[
   9, 10, 12, 18, 20, 20
   \]
   The median of this subset is the average of the 3rd and 4th values: 
   \[
   Q1 = \frac{12 + 18}{2} = 15
   \]

3. **Median (Q2)**: The median of the entire dataset is the middle value(s). Since we have 12 numbers, the median is the average of the 6th and 7th values:
   \[
   Q2 = \frac{20 + 27}{2} = 23.5
   \]

4. **Upper quartile (Q3)**: The upper quartile is the median of the upper half of the data (excluding the overall median). The upper half of the dataset is:
   \[
   27, 28, 29, 29, 35, 36
   \]
   The median of this subset is the average of the 3rd and 4th values: 
   \[
   Q3 = \frac{29 + 29}{2} = 29
   \]

5. **Maximum**: The largest value in the dataset is **36**.

### Interquartile Range (IQR):

The interquartile range is the difference between the upper quartile (Q3) and the lower quartile (Q1):
\[
IQR = Q3 - Q1 = 29 - 15 = 14
\]

### Summary:

- **Minimum**: 9
- **Lower quartile (Q1)**: 15
- **Median (Q2)**: 23.5
- **Upper quartile (Q3)**: 29
- **Maximum**: 36
- **Interquartile range (IQR)**: 14

Would you like further explanation or more details on quartiles?

Here are 5 related questions:
1. How are quartiles used to detect outliers in a data set?
2. Can the interquartile range ever be negative?
3. What is the significance of the interquartile range in statistics?
4. How would the five-number summary change if an additional value is added to the dataset?
5. How does the five-number summary differ from measures like mean and standard deviation?

**Tip**: The interquartile range is a robust measure of spread, less affected by extreme values than the range or standard deviation!

The following are the distances (in miles) to the nearest airport for 12 families. 9,10,12,18,20,20,27,28,29,29,35,36. Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.

Calculate the five-number summary and interquartile range for the dataset: 9, 10, 12, 18, 20, 20, 27, 28, 29, 29, 35, 36. This problem includes determining the minimum, lower quartile, median, upper quartile, maximum, and IQR, essential concepts in descriptive statistics for Grades 6-8.

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