Current Attempt in Progress The following set of data is given. (a) Find the mean \( \bar{x} \). Round your answer to one decimal place. \( \bar{x}=i, 30,37,41,47,47,55,57,92 \) (b) Find the median m. \( m=i \)

Sure, I'd be happy to help you find the mean and median of your data set. Let's break it down step by step. ### Given Data Set: \[ 30,\ 37, \ 41, \ 47, \ 47, \ 55, \ 57, \ 92 \] There are **8** data points in total. --- ### (a) Finding the Mean (\( \bar{x} \)) **Formula for Mean:** \[ \bar{x} = \frac{\sum x_i}{n} \] Where: - \( \sum x_i \) is the sum of all data points. - \( n \) is the number of data points. **Step-by-Step Calculation:** 1. **Sum of the Data Points:** \[ 30 + 37 + 41 + 47 + 47 + 55 + 57 + 92 = 406 \] 2. **Number of Data Points (\( n \)):** \[ n = 8 \] 3. **Calculate the Mean:** \[ \bar{x} = \frac{406}{8} = 50.75 \] 4. **Round to One Decimal Place:** \[ \bar{x} = 50.8 \] **Final Answer:** \[ \bar{x} = 50.8 \] --- ### (b) Finding the Median (\( m \)) **Understanding Median:** - **Median** is the middle value in an ordered data set. - If the number of data points (\( n \)) is **even**, the median is the average of the two middle numbers. **Step-by-Step Calculation:** 1. **Ordered Data Set:** \[ 30,\ 37,\ 41,\ 47,\ 47,\ 55,\ 57,\ 92 \] *(Already ordered in ascending order)* 2. **Number of Data Points (\( n \)):** \[ n = 8 \] 3. **Identify the Middle Two Numbers:** - Since \( n \) is even, the two middle numbers are the 4th and 5th data points. \[ 4^{th} \text{ data point} = 47 \] \[ 5^{th} \text{ data point} = 47 \] 4. **Calculate the Median:** \[ m = \frac{47 + 47}{2} = \frac{94}{2} = 47 \] **Final Answer:** \[ m = 47 \] --- ### Summary - **Mean (\( \bar{x} \))**: 50.8 - **Median (\( m \))**: 47 Feel free to reach out if you have any more questions or need further clarification!