https://file.aiquickdraw.com/mathbot/file/1730518617204vepbubuj.jpg

To determine the five-number summary and interquartile range for this data set, I'll go through each component.

### Data Set
The scores are:
56, 57, 59, 61, 61, 64, 69, 70, 73, 74, 77, 82, 82, 91

Since there are 14 data points, the steps are as follows:

### Step 1: Minimum and Maximum
- **Minimum**: 56
- **Maximum**: 91

### Step 2: Median (Middle Value)
- With 14 values, the median will be the average of the 7th and 8th values (when ordered).
- **Median** = (69 + 70) / 2 = 69.5

### Step 3: Lower Quartile (Q1)
- The lower quartile, Q1, is the median of the first half of the data (first 7 values).
- First half: 56, 57, 59, 61, 61, 64, 69
- **Lower Quartile (Q1)** = 59

### Step 4: Upper Quartile (Q3)
- The upper quartile, Q3, is the median of the second half of the data (last 7 values).
- Second half: 70, 73, 74, 77, 82, 82, 91
- **Upper Quartile (Q3)** = 77

### Step 5: Interquartile Range (IQR)
- The IQR is the difference between Q3 and Q1.
- **Interquartile Range (IQR)** = Q3 - Q1 = 77 - 59 = 18

### Final Summary
Here's the five-number summary and interquartile range for the data set:

- **Minimum**: 56
- **Lower Quartile (Q1)**: 59
- **Median**: 69.5
- **Upper Quartile (Q3)**: 77
- **Maximum**: 91
- **Interquartile Range (IQR)**: 18

Would you like more details on any of these steps or have any questions?

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### Related Questions
1. How do you calculate the median in a data set with an odd number of values?
2. What does the interquartile range tell you about the data spread?
3. How is the five-number summary helpful in data analysis?
4. How would the five-number summary change if an outlier were added to the data set?
5. Can the median ever be one of the quartiles?

### Tip
The interquartile range (IQR) is useful for identifying the spread of the middle 50% of data and is often used to detect outliers.

Give the five-number summary and the interquartile range for the data set: 56, 57, 59, 61, 61, 64, 69, 70, 73, 74, 77, 82, 82, 91.

Learn how to find the five-number summary (minimum, Q1, median, Q3, maximum) and interquartile range (IQR) for a set of test scores. This example covers concepts in descriptive statistics for Grades 6-8.

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