on 40 . Calculate the mean, the median, and the mode for each of the following data sets. a. \( 3,7,7,8,6,7,12,4 \) b. \( 10.5,12.5,12.5,14.5,19.5,16.5,12.5,14.5,11.5 \)

Sure, let's calculate the **mean**, **median**, and **mode** for each of the provided data sets. --- ### **a. Data Set: \( 3, 7, 7, 8, 6, 7, 12, 4 \)** #### **1. Mean** The **mean** is the average of all the numbers in the data set. \[ \text{Mean} = \frac{\sum \text{All Data Points}}{\text{Number of Data Points}} \] \[ \text{Mean} = \frac{3 + 7 + 7 + 8 + 6 + 7 + 12 + 4}{8} = \frac{54}{8} = 6.75 \] #### **2. Median** The **median** is the middle value when the data points are arranged in ascending order. If there's an even number of data points, it's the average of the two middle numbers. First, arrange the data in ascending order: \[ 3, 4, 6, 7, 7, 7, 8, 12 \] Since there are **8** data points (even number), the median is the average of the 4th and 5th terms. \[ \text{Median} = \frac{7 + 7}{2} = 7 \] #### **3. Mode** The **mode** is the number that appears most frequently in the data set. Looking at the data: \[ 3, 4, 6, 7, 7, 7, 8, 12 \] - **7** appears **3** times. - All other numbers appear fewer times. \[ \text{Mode} = 7 \] --- ### **b. Data Set: \( 10.5, 12.5, 12.5, 14.5, 19.5, 16.5, 12.5, 14.5, 11.5 \)** #### **1. Mean** \[ \text{Mean} = \frac{10.5 + 12.5 + 12.5 + 14.5 + 19.5 + 16.5 + 12.5 + 14.5 + 11.5}{9} \] Calculating the sum: \[ 10.5 + 12.5 = 23 \\ 23 + 12.5 = 35.5 \\ 35.5 + 14.5 = 50 \\ 50 + 19.5 = 69.5 \\ 69.5 + 16.5 = 86 \\ 86 + 12.5 = 98.5 \\ 98.5 + 14.5 = 113 \\ 113 + 11.5 = 124.5 \] \[ \text{Mean} = \frac{124.5}{9} \approx 13.83 \] #### **2. Median** First, arrange the data in ascending order: \[ 10.5, 11.5, 12.5, 12.5, 12.5, 14.5, 14.5, 16.5, 19.5 \] Since there are **9** data points (odd number), the median is the 5th term. \[ \text{Median} = 12.5 \] #### **3. Mode** The **mode** is the number that appears most frequently in the data set. Looking at the data: \[ 10.5, 11.5, 12.5, 12.5, 12.5, 14.5, 14.5, 16.5, 19.5 \] - **12.5** appears **3** times. - **14.5** appears **2** times. - All other numbers appear fewer times. \[ \text{Mode} = 12.5 \] --- ### **Summary** | Data Set | Mean | Median | Mode | |----------|------|--------|------| | a. \( 3, 7, 7, 8, 6, 7, 12, 4 \) | 6.75 | 7 | 7 | | b. \( 10.5, 12.5, 12.5, 14.5, 19.5, 16.5, 12.5, 14.5, 11.5 \) | ≈13.83 | 12.5 | 12.5 | --- If you have any further questions or need additional explanations, feel free to ask!