3:28 AM Thu Jan 23 Done Distances of Stars Of the 25 brightest stars, the distances from earth (in light-years) for some of those with distances less than 100 light-years are found below. Find the mean, median, mode, and midrange for the data. \( 36.7 \quad 11.4 \quad 8.6 \quad 16.8 \quad 42.2 \quad 33.7 \quad 25.1 \quad 4.4 \quad 51.5 \quad 25.3 \) Send data to Excel Part: \( \mathbf{0} / \mathbf{4} \) Part 1 of 4 Find the mean. Rounding rule for the mean: round to one more decimal place than the data as needed. Mean:

To find the **mean** distance of the given stars, follow these steps: ### **Data Provided:** \( 36.7, \; 11.4, \; 8.6, \; 16.8, \; 42.2, \; 33.7, \; 25.1, \; 4.4, \; 51.5, \; 25.3 \) (all in light-years) ### **Step 1: Calculate the Sum of All Data Points** \[ 36.7 + 11.4 + 8.6 + 16.8 + 42.2 + 33.7 + 25.1 + 4.4 + 51.5 + 25.3 = 255.7 \text{ light-years} \] ### **Step 2: Determine the Number of Data Points** \[ \text{Number of stars} = 10 \] ### **Step 3: Compute the Mean** \[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Data Points}} = \frac{255.7}{10} = 25.57 \text{ light-years} \] ### **Rounding Rule Applied:** - **Data Precision:** Each data point is given to **one decimal place**. - **Mean Precision:** According to the rounding rule, the mean should be rounded to **one more decimal place** than the data. Therefore, the mean is rounded to **two decimal places**. ### **Final Answer:** \[ \boxed{25.57 \text{ light-years}} \]