To find the mean and median number of board games played by the students, we need to process the data provided.
### Step 1: Understanding the Data
The table shows:
- 5 students played 0 board games
- 6 students played 1 board game
- 3 students played 2 board games
- 1 student played 3 board games
### Step 2: Convert the Table into a List of Observations
First, let's list out all the responses based on the given frequencies:
[tex]\[ \text{board\_games} = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3] \][/tex]
### Step 3: Calculate the Mean
The mean is the sum of all observations divided by the number of observations.
#### Total Sum:
[tex]\[ 0 \times 5 + 1 \times 6 + 2 \times 3 + 3 \times 1 \][/tex]
[tex]\[ = 0 + 6 + 6 + 3 \][/tex]
[tex]\[ = 15 \][/tex]
#### Total Number of Observations:
[tex]\[ 5 + 6 + 3 + 1 = 15 \][/tex]
#### Mean Calculation:
[tex]\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Total Number of Observations}} = \frac{15}{15} = 1.0 \][/tex]
### Step 4: Calculate the Median
The median is the middle value of the ordered list of observations. Since we have 15 observations (an odd number), the median will be the 8th value (as [tex]\( \frac{15 + 1}{2} = 8 \)[/tex]).
#### Ordered List of Observations:
[tex]\[ [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3] \][/tex]
The 8th value in this ordered list is 1.
### Final Answers:
[tex]\[ \text{Mean } = 1.0 \][/tex]
[tex]\[ \text{Median } = 1 \][/tex]
