Questions: Example C. Find the median with an even-numbered sample size. Find the median with an 8th student added to the previous Drake data. those two numbers or the number that is halfway between them. 0,5,6, 8, 10,12,14,15 Arrange the list in order from least to greatest. The median is 9 There are two middle numbers 8 10. The number halfway between these two numbers is 9. Find the mean and median of each sample data set. 1. Amount of hours spent playing video games per day by seven students. 3,6,0,2,5,1,8 Mean = Median = 2. Number of hours spent on Snapchat per week by six students. 3,2,0,4,5,4 Mean = Median =

Solution Steps

Given the data set representing the amount of hours spent playing video games per day by seven students: \[ 3, 6, 0, 2, 5, 1, 8 \]

The mean (\(\mu\)) is calculated as: \[ \mu = \frac{\sum_{i=1}^{n} x_i}{n} \] where \( n = 7 \) and \( x_i \) are the data points.

\[ \mu = \frac{3 + 6 + 0 + 2 + 5 + 1 + 8}{7} = \frac{25}{7} \approx 3.57 \]

To find the median, we first arrange the data in ascending order: \[ 0, 1, 2, 3, 5, 6, 8 \]

Since the number of data points (\(n = 7\)) is odd, the median is the middle value: \[ \text{Median} = x_{\left(\frac{n+1}{2}\right)} = x_4 = 3 \]

Given the data set representing the number of hours spent on Snapchat per week by six students: \[ 3, 2, 0, 4, 5, 4 \]

The mean (\(\mu\)) is calculated as: \[ \mu = \frac{\sum_{i=1}^{n} x_i}{n} \] where \( n = 6 \) and \( x_i \) are the data points.

\[ \mu = \frac{3 + 2 + 0 + 4 + 5 + 4}{6} = \frac{18}{6} = 3 \]

To find the median, we first arrange the data in ascending order: \[ 0, 2, 3, 4, 4, 5 \]

Since the number of data points (\(n = 6\)) is even, the median is the average of the two middle values: \[ \text{Median} = \frac{x_{\left(\frac{n}{2}\right)} + x_{\left(\frac{n}{2} + 1\right)}}{2} = \frac{x_3 + x_4}{2} = \frac{3 + 4}{2} = 3.5 \]

Final Answer