Let's analyze the question step by step: ### **Given Data** The number of times each of 10 workers has eaten an evening meal at a restaurant: ``` 5, 0, 7, 9, 8, 5, 5, 2, 2, 6 ``` Let's sort the data: ``` 0, 2, 2, 5, 5, 5, 6, 7, 8, 9 ``` ### **Statements Analysis** #### **Option 1:** > The number of times each worker has eaten an evening meal at a restaurant is a continuous variable. - **Explanation:** A continuous variable can take any value within a range (like height, weight), but the number of times is a countable, discrete variable. - **Conclusion:** **False** #### **Option 2:** > The position of the first quartile (Q1) is at 2.5. - **Explanation:** For \( n = 10 \), the position of \( Q_1 \) is \( \frac{n+1}{4} = \frac{11}{4} = 2.75 \). - **Conclusion:** **False** #### **Option 3:** > The value that represents the third quartile (Q3 percentile-75th) is 8.25. - **Calculation:** \( Q_3 \) position = \( 0.75 \times (n+1) = 0.75 \times 11 = 8.25 \) This is between the 8th and 9th values in the sorted list (7 and 8): \[ Q_3 = 7 + 0.25 \times (8-7) = 7 + 0.25 = 7.25 \] - **Conclusion:** **False** #### **Option 4:** > The mean is 5.6. - **Calculation:** \[ \text{Mean} = \frac{0+2+2+5+5+5+6+7+8+9}{10} = \frac{49}{10} = 4.9 \] - **Conclusion:** **False** #### **Option 5:** > The median is 5.97. - **Calculation:** For 10 values, the median is the average of the 5th and 6th values. 5th value: 5 6th value: 5 \[ \text{Median} = \frac{5+5}{2} = 5 \] - **Conclusion:** **False** ### **Final Answer** #### **None of the provided statements are correct.** --- #### **Summary Table** | Option | Statement | Conclusion | |--------|-----------|------------| | 1 | Continuous variable? | False | | 2 | Q1 position at 2.5? | False | | 3 | Q3 value is 8.25? | False | | 4 | Mean is 5.6? | False | | 5 | Median is 5.97? | False | --- Let me know if you want the correct calculations for quartiles or any other part explained!

## Step-by-Step Solution ### **Given Data** The number of times each of 10 workers has eaten an evening meal at a restaurant: ``` 5, 0, 9, 1, 9, 8, 5, 5, 2, 6 ``` ### **Step 1: Sort the Data** First, we sort the data in ascending order: ``` 0, 1, 2, 5, 5, 5, 6, 8, 9, 9 ``` ### **Step 2: Analyze Statements** #### **Option 1: Continuous Variable** - **Explanation:** A continuous variable can take any value within a range. The number of times eaten is discrete. - **Conclusion:** **False** #### **Option 2: Position of First Quartile (Q1)** - **Calculation:** For \( n = 10 \), the position of \( Q_1 \) is calculated as: \[ Q_1 \text{ Position} = \frac{n+1}{4} = \frac{11}{4} = 2.75 \] - The 2.75th position is between the 2nd and 3rd values (1 and 2). - **Conclusion:** **False** #### **Option 3: Value of Third Quartile (Q3)** - **Calculation:** The position of \( Q_3 \): \[ Q_3 \text{ Position} = 0.75 \times (n+1) = 0.75 \times 11 = 8.25 \] - The 8.25th position is between the 8th and 9th values (8 and 9): \[ Q_3 = 8 + 0.25 \times (9 - 8) = 8 + 0.25 = 8.25 \] - **Conclusion:** **True** #### **Option 4: Mean Calculation** - **Calculation:** \[ \text{Mean} = \frac{0 + 1 + 2 + 5 + 5 + 5 + 6 + 8 + 9 + 9}{10} = \frac{50}{10} = 5 \] - **Conclusion:** **False** #### **Option 5: Median Calculation** - **Calculation:** For 10 values, the median is the average of the 5th and 6th values: \[ \text{Median} = \frac{5 + 5}{2} = 5 \] - **Conclusion:** **False** ### **Final Answer** - **Only Option 3 is correct:** The value that represents the third quartile (Q3) is 8.25. --- ### **Summary Table** | Option | Statement | Conclusion | |--------|---------------------------------------------|------------| | 1 | Continuous variable? | False | | 2 | Q1 position at 2.75? | False | | 3 | Q3 value is 8.25? | True | | 4 | Mean is 5? | False | | 5 | Median is 5.97? | False | Feel free to ask if you need further explanations or calculations!