To determine whether the mean or the median best describes the dataset, we first calculate both values for the provided free throw data:
Game Free Throws:
- Game 1: 12
- Game 2: 5
- Game 3: 8
- Game 4: 18
- Game 5: 10
- Game 6: 11
- Game 7: 6
Step 1: Calculate the Mean
To calculate the mean, sum all the free throws and then divide by the number of games:
\[ \text{Mean} = \frac{(12 + 5 + 8 + 18 + 10 + 11 + 6)}{7} \] \[ \text{Mean} = \frac{70}{7} = 10 \]
Step 2: Calculate the Median
To calculate the median, arrange the free throws in ascending order:
5, 6, 8, 10, 11, 12, 18
Since there are 7 numbers (an odd count), the median is the middle value, which is the 4th number:
\[ \text{Median} = 10 \]
Step 3: Analyze the Distribution Shape
Now, let's consider the values:
- The dataset is: 5, 6, 8, 10, 11, 12, 18
- The minimum value is 5 and the maximum is 18.
The distribution is slightly skewed to the right because of the higher value (18). However, both the mean and median are equal in this case at 10.
Conclusion:
Since the mean and median are both equal and close to the central values of the dataset, either could be used to describe the dataset reasonably well. However, using the median is often preferred in skewed distributions as it is less affected by outliers. Thus, while in this specific case the mean is accurate, the median would be the more robust measure to describe the dataset's central tendency.