Five number summary of 3.5,4,4.6,6,6.8,7.2,7.5,8,8,9,10,11

To calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

**Data (sorted):**  
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

### 1. **Minimum:**  
The smallest value in the dataset is **3.5**.

### 2. **First Quartile (Q1):**  
Q1 is the median of the lower half of the data.  
Lower half of the dataTo calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

**Data (sorted):**  
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

### 1. **Minimum:**  
The smallest value in the dataset is **3.5**.

### 2. **First Quartile (Q1):**  
Q1 is the median of the lower half of the data.  
Lower half of the  3.5, 4, 4.6, 6, 6.8, 7.2  
Median of the lower half: \((4.6 + 6)/2 = 5.3\)

So, **Q1 = 5.3**.

### 3. **Median:**  
The median is the middle value of the entire dataset.  
Middle value: \(7.2\) (since it's the 7th value in the sorted list).

So, **Median = 7.2**.

### 4. **Third Quartile (Q3):**  
Q3 is the median of the upper half of the data.  
Upper half of the dataTo calculate the five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum) of the given dataset:

**Data (sorted):**  
3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

### 1. **Minimum:**  
The smallest value in the dataset is **3.5**.

### 2. **First Quartile (Q1):**  
Q1 is the median of the lower half of the data.  
Lower half of the  3.5, 4, 4.6, 6, 6.8, 7.2  
Median of the lower half: \((4.6 + 6)/2 = 5.3\)

So, **Q1 = 5.3**.

### 3. **Median:**  
The median is the middle value of the entire dataset.  
Middle value: \(7.2\) (since it's the 7th value in the sorted list).

So, **Median = 7.2**.

### 4. **Third Quartile (Q3):**  
Q3 is the median of the upper half of the data.  
Upper half of the  7.5, 8, 8, 9, 10, 11  
Median of the upper half: \((8 + 9)/2 = 8.5\)

So, **Q3 = 8.5**.

### 5. **Maximum:**  
The largest value in the dataset is **11**.

### **Five-Number Summary:**
- **Minimum = 3.5**
- **Q1 = 5.3**
- **Median = 7.2**
- **Q3 = 8.5**
- **Maximum = 11**

Would you like more details on this or any further questions?

### Related Questions:
1. How is the interquartile range (IQR) calculated from the five-number summary?
2. What does each component of the five-number summary represent in real-world contexts?
3. How do outliers affect the five-number summary?
4. How can the five-number summary be used to construct a box plot?
5. How can you calculate the mean and standard deviation of the same dataset?

**Tip:** The interquartile range (IQR) is a measure of the spread of the middle 50% of the data and is found by subtracting Q1 from Q3.

Five number summary of 3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11

Learn how to calculate the five-number summary for the data set 3.5, 4, 4.6, 6, 6.8, 7.2, 7.5, 8, 8, 9, 10, 11. This problem covers concepts like the minimum, first quartile, median, third quartile, and maximum, essential for understanding descriptive statistics. Suitable for Grades 6-8.

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