Final answer:
The mode indicates the most common values in a data set, while the mean is the average that can be skewed by outliers. The median is the middle value and less influenced by extremes. Standard deviation measures how widely data values are spread around the mean.
Step-by-step explanation:
The mode is a measure of the center of the data that represents the most frequently occurring values within a data set. The data set can be bimodal if it has two values that occur with the highest frequency.
For skewed distributions, the mean, which is the arithmetic average of the data, can be pulled towards the tail of the distribution and reflects the skewness the most. If a data set contains extreme values or outliers, the median is preferable as it is less impacted by these values. Measures of the spread of the data, like the standard deviation, tell us about the variation in the data set, indicating how far data values tend to be from the mean.
When assessing which measure is more valuable in decision-making scenarios, such as building a new community college, it depends on the context. The mode would tell you the most common enrollment size among existing schools, which can be valuable if that size is particularly suited to the local population or economy. The mean, on the other hand, gives you the average enrollment size, which could be useful in estimating the expected size and resource needs for the new college.