2. Find the median and mode of the following data: \( 5,10,5,15,5,20 \)

To find the median and mode of the data set \( 5, 10, 5, 15, 5, 20 \), we will follow these steps: ### Step 1: Find the Mode The mode is the number that appears most frequently in a data set. In the given data: - \( 5 \) appears \( 3 \) times - \( 10 \) appears \( 1 \) time - \( 15 \) appears \( 1 \) time - \( 20 \) appears \( 1 \) time Since \( 5 \) appears the most frequently, the mode is: \[ \text{Mode} = 5 \] ### Step 2: Find the Median To find the median, we first need to arrange the data in ascending order: \[ 5, 5, 5, 10, 15, 20 \] Since there are \( 6 \) numbers in the data set (an even number), the median will be the average of the two middle numbers. The two middle numbers in this ordered list are the \( 3^{rd} \) and \( 4^{th} \) numbers: - \( 3^{rd} \) number: \( 5 \) - \( 4^{th} \) number: \( 10 \) Now, we calculate the median: \[ \text{Median} = \frac{5 + 10}{2} = \frac{15}{2} = 7.5 \] ### Summary - **Mode**: \( 5 \) - **Median**: \( 7.5 \)