What is the five number summary for this data set: 130,120,135,125,120,125,141,130,140,125,135,140,139,150

To find the five-number summary for the dataset:

130, 120, 135, 125, 120, 125, 141, 130, 140, 125, 135, 140, 139, 150

We need to calculate the following:

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

### Step-by-step process:
1. Sort the dataTo find the five-number summary for the dataset:

130, 120, 135, 125, 120, 125, 141, 130, 140, 125, 135, 140, 139, 150

We need to calculate the following:

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

### Step-by-step process:
1. Sort the 
   120, 120, 125, 125, 125, 130, 130, 135, 135, 139, 140, 140, 141, 150

2. **Minimum** = 120

3. **Median (Q2)**:
   Since there are 14 data points, the median is the average of the 7th and 8th values:
   \( \text{Median} = \frac{130 + 135}{2} = 132.5 \)

4. **Q1 (First Quartile)**:
   The lower half of the data is: 120, 120, 125, 125, 125, 130, 130
   The median of this lower half is the 4th value: Q1 = 125

5. **Q3 (Third Quartile)**:
   The upper half of the data is: 135, 139, 140, 140, 141, 150
   The median of this upper half is the 11th value: Q3 = 140

6. **Maximum** = 150

### Final Five-Number Summary:
- Minimum: 120
- Q1: 125
- Median: 132.5
- Q3: 140
- Maximum: 150

Would you like more details or have any questions?

Here are 5 related questions:
1. How is the interquartile range (IQR) calculated using the five-number summary?
2. What are outliers, and how can the five-number summary help in identifying them?
3. How does the five-number summary differ from the mean and standard deviation?
4. What does the median tell us about the skewness of this dataset?
5. How can you visualize a five-number summary using a boxplot?

**Tip**: When calculating the quartiles, always ensure that your dataset is sorted in ascending order for accurate results.

Find the five-number summary for the dataset 130, 120, 135, 125, 120, 125, 141, 130, 140, 125, 135, 140, 139, 150. This includes calculating the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. A detailed step-by-step breakdown of the solution is provided, ideal for students in Grades 6-8.

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