find the five number summary for the data set : 123, 148, 125, 148, 129, 150, 132, 151, 133, 154, 135, 161, 138, 163, 139, 163, 143, 166, 146, 173

The five-number summary consists of the following:

1. **Minimum**: The smallest number in the dataset.
2. **First Quartile (Q1)**: The 25th percentile, marking the first quarter of the dataset.
3. **Median (Q2)**: The 50th percentile, or the middle number of the dataset.
4. **Third Quartile (Q3)**: The 75th percentile, marking the third quarter of the dataset.
5. **Maximum**: The largest number in the dataset.

### Steps:
1. **Order the data from smallest to largest**:
   \[
   123, 125, 129, 132, 133, 135, 138, 139, 143, 146, 148, 148, 150, 151, 154, 161, 163, 163, 166, 173
   \]
   
2. **Find the five-number summary**:

- **Minimum**: 123
- **Maximum**: 173
- **Median (Q2)**: The median is the middle value. Since there are 20 numbers (even), the median is the average of the 10th and 11th values:
  \[
  \text{Median} = \frac{146 + 148}{2} = 147
  \]

- **First Quartile (Q1)**: This is the median of the first half (numbers before the median):
  \[
  123, 125, 129, 132, 133, 135, 138, 139, 143, 146
  \]
  The middle value is between 135 and 138:
  \[
  Q1 = \frac{135 + 138}{2} = 136.5
  \]

- **Third Quartile (Q3)**: This is the median of the second half (numbers after the median):
  \[
  148, 150, 151, 154, 161, 163, 163, 166, 173
  \]
  The middle value is between 154 and 161:
  \[
  Q3 = \frac{154 + 161}{2} = 157.5
  \]

### The five-number summary is:
- **Minimum**: 123
- **Q1**: 136.5
- **Median (Q2)**: 147
- **Q3**: 157.5
- **Maximum**: 173

Would you like more details on any step?

### Related Questions:
1. What is the interquartile range (IQR) for this data set?
2. How do outliers affect the five-number summary?
3. Can the five-number summary be used to compare different data sets?
4. How is the five-number summary represented on a box plot?
5. What other measures of central tendency can be used in place of the median?

### Tip:
The interquartile range (IQR) is a good measure of spread that is resistant to outliers. It is calculated as \( Q3 - Q1 \).

Find the five number summary for the data set: 123, 148, 125, 148, 129, 150, 132, 151, 133, 154, 135, 161, 138, 163, 139, 163, 143, 166, 146, 173

Find the five-number summary for the data set: 123, 148, 125, 148, 129, 150, 132, 151, and more. This solution provides the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Ideal for students in Grades 6-8, this step-by-step guide explains key concepts in descriptive statistics.

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