6.) How does the mode change after adding the value " 18 " to the data set? Increase, decrease, or no change? \( 20,14,10,15,15,14,19,15 \) 9.) Find the range.

Calculate the value by following steps: - step0: Calculate: \(20-10\) - step1: Subtract the numbers: \(10\) Let's solve the problems step by step. ### Problem 6: Mode Change After Adding 18 1. **Current Data Set**: \( 20, 14, 10, 15, 15, 14, 19, 15 \) 2. **Identify the Mode**: The mode is the number that appears most frequently in a data set. - In the current data set, the number \( 15 \) appears three times, while \( 14 \) appears twice, and all other numbers appear once. Thus, the mode is \( 15 \). 3. **Add the Value 18**: Now the data set becomes \( 20, 14, 10, 15, 15, 14, 19, 15, 18 \). 4. **Identify the New Mode**: - In the new data set, \( 15 \) still appears three times, while \( 14 \) appears twice, and \( 18 \) appears once. Therefore, the mode remains \( 15 \). ### Conclusion for Problem 6: - **Mode Change**: There is **no change** in the mode after adding the value \( 18 \). --- ### Problem 9: Find the Range 1. **Current Data Set**: \( 20, 14, 10, 15, 15, 14, 19, 15 \) 2. **Calculate the Range**: The range is calculated as the difference between the maximum and minimum values in the data set. - Maximum value: \( 20 \) - Minimum value: \( 10 \) 3. **Calculate the Range**: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 20 - 10 = 10 \] ### Conclusion for Problem 9: - **Range**: The range of the data set is \( 10 \). In summary: - The mode does not change after adding \( 18 \). - The range of the data set is \( 10 \).