\begin{tabular}{l} Distances of Stars Of the 25 brightest stars, the distances from earth (in light-years) for some of those with distances le \\ 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 1 of 4 \\ Find the mean. \\ Rounding rule for the mean: round to one more decimal place than the data as needed. \\ Mean: 25.57 \\ Part 2 of 4 \\ Find the mode(s). \\ Find the median. \\ Mere is more than one mode, separate them with commas. Select "None" if applicable. \\ Part 3 of 4 \\ Alternate Answer: \\ Part: 25.20 \\ \hline\end{tabular}

Sure, let's analyze the given data set to find the **mean**, **median**, **mode**, and **midrange**. Here's a step-by-step breakdown: ### **Given Data (Distances in Light-Years):** \[ 36.7, \, 11.4, \, 8.6, \, 16.8, \, 42.2, \, 33.7, \, 25.1, \, 4.4, \, 51.5, \, 25.3 \] ### **1. Mean** The **mean** (average) has already been calculated as **25.57**. ### **2. Mode** The **mode** is the value that appears most frequently in the data set. - **Frequency of Each Value:** - 4.4: 1 - 8.6: 1 - 11.4: 1 - 16.8: 1 - 25.1: 1 - 25.3: 1 - 33.7: 1 - 36.7: 1 - 42.2: 1 - 51.5: 1 - **Conclusion:** All values appear **once**. Therefore, there is **no mode**. **Mode:** **None** ### **3. Median** The **median** is the middle value when the data set is ordered from smallest to largest. - **Ordered Data:** \[ 4.4, \, 8.6, \, 11.4, \, 16.8, \, 25.1, \, 25.3, \, 33.7, \, 36.7, \, 42.2, \, 51.5 \] - **Number of Data Points:** 10 (even number) - **Finding the Median:** - The median is the average of the 5th and 6th values. - 5th value: **25.1** - 6th value: **25.3** \[ \text{Median} = \frac{25.1 + 25.3}{2} = \frac{50.4}{2} = 25.2 \] **Median:** **25.20** ### **4. Midrange** The **midrange** is the average of the smallest and largest values in the data set. - **Smallest Value:** 4.4 - **Largest Value:** 51.5 \[ \text{Midrange} = \frac{4.4 + 51.5}{2} = \frac{55.9}{2} = 27.95 \] **Midrange:** **27.95** ### **Summary of Results** - **Mean:** 25.57 - **Median:** 25.20 - **Mode:** None - **Midrange:** 27.95 If you need to input these results into Excel or require further assistance with any of the parts, feel free to ask!