Final answer:
Extremely large or small values most significantly affect the mean, as it is the measure of central tendency that takes into account all values in the dataset, making it sensitive to outliers. The median is less affected since it only considers the middle value, and the mode, being the most frequent value, may remain unchanged unless the outlier is frequent.
Step-by-step explanation:
Extremely large or extremely small values affect the mean the most out of the three measures of central tendency (mean, median, and mode). The mean takes into account the actual values in the dataset and will be skewed by outliers, which can be extremely large or extremely small values. The median, being the middle value when a data set is ordered from smallest to largest, is less affected by outliers than the mean. The mode, which is the most frequently occurring value in a data set, may not change at all in the presence of outliers unless the outlier itself occurs most frequently.
Therefore, if a data set has a skew due to extreme values, the mean will often be pulled toward the direction of the skew (greater than or less than the median), especially in a skewed distribution. However, the median and mode will be less influenced. In symmetric distributions, the mean, median, and mode tend to be equal or very close, with no skewing effects.