0

0.26

2.82

2.45

0.38

2.92

0.84

0.81

0.14

0.48

0

0.67

2.84

0.12

2.5

3.47

1.26

0.65

1.67

3.1

0

0.16

0

1.07

2.39

0.23

0.41

0.58
 what is the five number summary

To calculate the five-number summary, you need the following key statistics from the dataset:

1. **Minimum**: The smallest value in the dataset.
2. **First Quartile (Q1)**: The 25th percentile, or the median of the lower half of the dataset.
3. **Median (Q2)**: The middle value of the dataset.
4. **Third Quartile (Q3)**: The 75th percentile, or the median of the upper half of the dataset.
5. **Maximum**: The largest value in the dataset.

Let's calculate the five-number summary for the provided dataTo calculate the five-number summary, you need the following key statistics from the dataset:

1. **Minimum**: The smallest value in the dataset.
2. **First Quartile (Q1)**: The 25th percentile, or the median of the lower half of the dataset.
3. **Median (Q2)**: The middle value of the dataset.
4. **Third Quartile (Q3)**: The 75th percentile, or the median of the upper half of the dataset.
5. **Maximum**: The largest value in the dataset.

Let's calculate the five-number summary for the provided 

### Data (sorted):
0, 0, 0, 0, 0.12, 0.14, 0.16, 0.23, 0.26, 0.38, 0.41, 0.48, 0.58, 0.65, 0.67, 0.81, 0.84, 1.07, 1.26, 1.67, 2.39, 2.45, 2.5, 2.82, 2.84, 2.92, 3.1, 3.47

### 1. Minimum:
- **0**

### 2. First Quartile (Q1):
- The lower half of the data has 14 values:  
  0, 0, 0, 0, 0.12, 0.14, 0.16, 0.23, 0.26, 0.38, 0.41, 0.48, 0.58, 0.65  
  The median of this lower half is between 0.23 and 0.26, so:  
  **Q1 = 0.245**

### 3. Median (Q2):
- The median of the entire dataset (28 values) is between the 14th and 15th values (0.65 and 0.67), so:  
  **Median = 0.66**

### 4. Third Quartile (Q3):
- The upper half of the data has 14 values:  
  0.67, 0.81, 0.84, 1.07, 1.26, 1.67, 2.39, 2.45, 2.5, 2.82, 2.84, 2.92, 3.1, 3.47  
  The median of this upper half is between 2.39 and 2.45, so:  
  **Q3 = 2.42**

### 5. Maximum:
- **3.47**

### Five-number summary:
- **Minimum** = 0
- **Q1** = 0.245
- **Median (Q2)** = 0.66
- **Q3** = 2.42
- **Maximum** = 3.47

Would you like more details or clarification on any part of the process?

Here are five related questions you might explore:
1. How do you calculate interquartile range (IQR) from the five-number summary?
2. What does the five-number summary tell us about the distribution of the data?
3. How does one create a boxplot using the five-number summary?
4. What role does the median play in understanding skewness?
5. How do outliers affect the five-number summary?

**Tip**: The interquartile range (IQR) is a great way to measure the spread of the middle 50% of your data, calculated as Q3 - Q1.

0, 0.26, 2.82, 2.45, 0.38, 2.92, 0.84, 0.81, 0.14, 0.48, 0, 0.67, 2.84, 0.12, 2.5, 3.47, 1.26, 0.65, 1.67, 3.1, 0, 0.16, 0, 1.07, 2.39, 0.23, 0.41, 0.58. What is the five number summary?

Learn how to calculate the five-number summary for the dataset: 0, 0.26, 2.82, 2.45, 0.38, and more. This example covers the key concepts of descriptive statistics, including how to find the minimum, quartiles, median, and maximum. Suitable for high school students in Grades 9-12.

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