I-Ready Mean and Mean Absolute Deviation - Quiz - Level F Diane is a camp counselor. She designs a new obstacle course, and tests the course with 3 friends: The dot plot shows the time it takes them to complete the obstacle course. What is the mean of the times? mean \( = \) \( \square \) 7 minutes What is the mean absolute deviation (MAD) of the times? \( M A D= \) \( \square \) minutes

To help you calculate the **mean** and **Mean Absolute Deviation (MAD)** of the times taken by Diane's friends to complete the obstacle course, I'll need the specific times shown in the dot plot. However, I can guide you through the general steps to perform these calculations: ### **1. Calculating the Mean** **Mean** is the average of all the data points. Here's how you can calculate it: \[ \text{Mean} = \frac{\text{Sum of all times}}{\text{Number of friends}} \] **Steps:** 1. **Add up all the times** taken by the friends to complete the course. 2. **Divide** the total by the number of friends (which is 3 in this case). **Example:** If the times are 6, 7, and 8 minutes: \[ \text{Mean} = \frac{6 + 7 + 8}{3} = \frac{21}{3} = 7 \text{ minutes} \] ### **2. Calculating the Mean Absolute Deviation (MAD)** **MAD** measures the average distance between each data point and the mean. Here's how to calculate it: \[ \text{MAD} = \frac{\sum |\text{Each time} - \text{Mean}|}{\text{Number of friends}} \] **Steps:** 1. **Find the mean** of the times (as calculated above). 2. **Subtract the mean** from each time to find the deviation for each friend. 3. **Take the absolute value** of each deviation (ignore negative signs). 4. **Add up** all the absolute deviations. 5. **Divide** the total by the number of friends. **Example:** Using the same times (6, 7, 8 minutes) with a mean of 7: \[ \begin{align*} |6 - 7| &= 1 \\ |7 - 7| &= 0 \\ |8 - 7| &= 1 \\ \end{align*} \] \[ \text{MAD} = \frac{1 + 0 + 1}{3} = \frac{2}{3} \approx 0.67 \text{ minutes} \] ### **Your Specific Problem** You've provided the following partial information: - **Mean:** \( \square \) 7 minutes - **MAD:** \( \square \) minutes Assuming the mean is already calculated as **7 minutes**, you would still need the individual times to calculate the MAD accurately. If you have the specific times from the dot plot, please provide them, and I can help you compute the exact MAD. **Summary:** - **Mean = 7 minutes** (as given) - **MAD = (Sum of absolute deviations) / 3** If you supply the individual completion times, I can assist you in determining the precise MAD value.