Final answer:
The most appropriate measure of central tendency for a data set depends on whether there are outliers or the data is skewed, with the median being preferable in such cases, and the mean being better for symmetrical distributions.
Step-by-step explanation:
When choosing the measure of central tendency that best describes a new data set including the number 30, we should consider whether the data has outliers or extreme values. If there are significant outliers or the data set is skewed, the median would be the most appropriate choice as it is less affected by extreme values. However, if the data set is roughly symmetrical, the mean would be a good choice as it would accurately reflect the central point of the data. The mode is the most frequently occurring value in the data set and would be useful if we have repeated values.
In a symmetrical distribution, the mean, median, and mode will all coincide or be very close to each other. Since the mean tends to be sensitive to skewness, for a data set with a few extreme values, the median might be preferable. It is important to analyze the shape of the data to determine the most appropriate measure of central tendency.