Select the correct answer.The table shows the number of hours Hazel worked per week at her part-time job for the last 20 weeks.9 22 16 12 16 10 22 16 17 8 20 18 10 20 25 6 14 10 14 20
Identify the five number summary (lowest value, first quartile, median, third quartile, and highest value) for the corresponding box plot.

To find the five-number summary (lowest value, first quartile, median, third quartile, and highest value) for the data set, we need to:

1. **Sort the data in ascending order**.
2. **Identify the lowest and highest values**.
3. **Determine the median**.
4. **Find the first quartile (Q1) and third quartile (Q3)**.

### Step 1: Sort the Data
Sorted dataTo find the five-number summary (lowest value, first quartile, median, third quartile, and highest value) for the data set, we need to:

1. **Sort the data in ascending order**.
2. **Identify the lowest and highest values**.
3. **Determine the median**.
4. **Find the first quartile (Q1) and third quartile (Q3)**.

### Step 1: Sort the Data
Sorted   
6, 8, 9, 10, 10, 10, 12, 14, 14, 16, 16, 16, 17, 18, 20, 20, 20, 22, 22, 25

### Step 2: Identify the Lowest and Highest Values
- **Lowest value (Min):** 6
- **Highest value (Max):** 25

### Step 3: Determine the Median
The median is the middle value of the sorted data. Since there are 20 data points, the median is the average of the 10th and 11th values.

- **Median:** \(\frac{16 + 16}{2} = 16\)

### Step 4: Find the First Quartile (Q1) and Third Quartile (Q3)
- **First Quartile (Q1):** The median of the first half of the data (before the overall median). This is the 5th and 6th data points' average.
  - Q1: \(\frac{10 + 10}{2} = 10\)

- **Third Quartile (Q3):** The median of the second half of the data (after the overall median). This is the 15th and 16th data points' average.
  - Q3: \(\frac{20 + 20}{2} = 20\)

### The Five-Number Summary:
- **Lowest Value:** 6
- **First Quartile (Q1):** 10
- **Median:** 16
- **Third Quartile (Q3):** 20
- **Highest Value:** 25

Would you like details or have any questions?

Here are some related questions you might find helpful:
1. How do you calculate the interquartile range (IQR) from a five-number summary?
2. What does the median tell you about a data set?
3. How can outliers be identified using a box plot?
4. What is the significance of the first and third quartiles in data analysis?
5. How does the five-number summary help in understanding the spread of data?
6. Can a box plot show more than just the five-number summary?
7. How do you interpret a box plot when comparing two data sets?
8. How does the five-number summary differ from the mean and standard deviation?

**Tip:** When interpreting data distributions, the five-number summary provides a quick snapshot of the data's central tendency, variability, and potential outliers.

Learn how to calculate the five-number summary (lowest value, first quartile, median, third quartile, and highest value) for a dataset using a step-by-step guide. This problem involves understanding descriptive statistics and box plots. Suitable for students in Grades 9-12.

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