Final answer:
The outlier in the given dataset is the number 48. Excluding this outlier will affect the mean the most because the mean is sensitive to all values in the dataset and will decrease significantly without the outlier, while the median and mode are less impacted.
Step-by-step explanation:
The dataset provided is: 12, 19, 19, 20, 21, 22, 22, 23, 24, 26, 27, 28, 29, 30, 32, 35, 48. First, we identify the outlier, which in this case is the number 48. This number is significantly higher than the rest and can be considered an outlier. Now, to answer the question of which measure of central tendency is affected the most by the outlier, we need to consider the effect on the mean, median, and mode when the outlier is excluded.
If we exclude the outlier, the mean will be affected the most. The mean takes into account all the values in the dataset, and when a high outlier is removed, the mean will decrease significantly. The median, being the middle value, will not change as it is less sensitive to extreme values, especially since our dataset has an even number of observations, thus the median is the average of the two middle values. The mode will not be affected at all, as it is simply the most frequently occurring value in the dataset. Therefore, the answer is A. mean.
In this dataset, excluding the outlier would result in a lower mean, while the median and mode would remain unchanged or be less impacted.