To determine whether the mean or median best represents the data set, we first need to calculate both values based on the goals scored in each of the 9 games.
The goals scored in each game are: 6, 1, 1, 0, 3, 1, 0, 3, 8.
Step 1: Calculate the Mean
To calculate the mean:
- Sum the total goals scored: \(6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8 = 23\)
- Divide the sum by the number of games (9): \[ \text{Mean} = \frac{23}{9} \approx 2.56 \]
Step 2: Calculate the Median
To find the median, we first need to order the goals scored: 0, 0, 1, 1, 1, 3, 3, 6, 8.
Since there are 9 data points (an odd number), the median is the middle value, which is the 5th number in the ordered list:
- The 5th value is 1.
Summary:
- Mean: approximately 2.56
- Median: 1
Step 3: Determine the Best Measure of Center
The data set is somewhat right-skewed due to the higher number of goals in some games (e.g., 8 in one game). When data is skewed, the median can often be a better measure of central tendency because it is less affected by extreme values.
Therefore, the median value of 1 is the best measure of center that describes the shape of the data set. Thus, the correct response is:
The median value of 1 is the best measure of center that describes the shape of the data set.