Final answer:
The mean (option a) is the statistical measure most affected by outliers. In a skewed dataset, the median or mode are preferable measures of the center because they are less influenced by extreme values.
Step-by-step explanation:
The statistical observation that is most significantly affected by outliers is the mean. Outliers are extreme values that differ significantly from other observations in the dataset. Since the mean is the arithmetic average of all the numbers in the set, adding a very high or very low outlier will shift the mean significantly more than it would the median or mode.
When examining the shape of the data, the median or the mode may give a more appropriate result than the mean if the data is skewed because they are less influenced by extreme values. The median is the middle value that separates the higher half from the lower half of the dataset and is unaffected by the magnitude of outliers, maintaining its position unless the number of observations changes. The mode is the most frequently occurring value in the data and does not change unless the frequency of values changes. By contrast, the standard deviation might also be affected by outliers but in a different way: it measures the amount of variation or dispersion from the mean, so an outlier would increase that dispersion measure.
When choosing an appropriate measure of center for a dataset that is skewed or contains outliers, the median or mode are generally preferred over the mean. This is because the median and mode are more robust to the skewness or extremity of the outliers, providing a better representation of the typical value in such datasets.