To determine whether the mean or median best describes the shape of the data set, we first need to calculate both the mean and the median of the free throws made.
Data Set: 4, 14, 5, 7, 19, 15, 6
Step 1: Calculate the Mean Mean = (Sum of all free throws) / (Number of games)
Sum = 4 + 14 + 5 + 7 + 19 + 15 + 6 = 70
Number of games = 7
Mean = 70 / 7 = 10
Step 2: Calculate the Median To find the median, we need to arrange the data in ascending order: 4, 5, 6, 7, 14, 15, 19
The median is the middle value. Since there are 7 values (an odd number), the median is the 4th value: Median = 7
Step 3: Determine Which is More Descriptive
- Mean = 10
- Median = 7
The mean (10) is higher than the median (7), indicating that the data may be skewed by the higher values, which can affect the mean more than the median. Since the mean is influenced by the outlier (19), the median is likely a better descriptor of the central tendency of this data set.
Therefore, the value that best describes the shape of the data set is:
2 (median)