To determine whether the mean or median is the best measure of center for the data set, we first need to calculate both the mean and median of the goals scored.
Data set: 6, 1, 1, 0, 3, 1, 0, 3, 8
Step 1: Calculate the mean
\[ \text{Mean} = \frac{\text{Sum of all goals}}{\text{Number of games}} = \frac{6 + 1 + 1 + 0 + 3 + 1 + 0 + 3 + 8}{9} = \frac{23}{9} \approx 2.56 \]
So, the mean value is approximately 2.6 (if rounded).
Step 2: Calculate the median
To find the median, we first need to sort the data set:
0, 0, 1, 1, 1, 3, 3, 6, 8
Since there are 9 values (an odd number), the median is the middle value, which is the 5th value in the sorted list.
Thus, the median is 1.
Step 3: Summary of the calculations
- Mean ≈ 2.6
- Median = 1
Final Decision:
In this case, the mean is affected by the outlier (the 8 goals in game 9), making it higher than most other scores. The median, being less sensitive to outliers, provides a better measure of the central tendency for the goals scored.
Between the two measures, the median value of 1 is the best measure of center that describes the shape of the data set.
Therefore, the answer is: The median value of 1 is the best measure of center that describes the shape of the data set.