Final answer:
Adding a large number to a data set is most likely to change the mean (A) since it is the arithmetic average and is sensitive to changes in data values. The median and mode are less affected by a single large value, with the median being a robust measure in the presence of outliers and the mode being dependent on frequency rather than magnitude.
Step-by-step explanation:
When you add a large number to a data set, the measure of central tendency that is most likely to change is the mean (A). The mean, also known as the arithmetic average, is calculated by summing all the values in the data set and then dividing by the number of values. Adding a large number can significantly increase the sum, which in turn will impact the calculated mean. As for the median (B), which is the middle value when the data is sorted from least to greatest, adding one large number may not affect it significantly, especially if the data set is large. The median is less sensitive to extreme values or outliers as it depends on the ordering of values rather than their magnitude.
The mode (C) is the value that occurs most frequently in a data set. Unless the large number added is already a frequently occurring value, the mode will not change. It is entirely reliant on frequency and not on the actual values. In the context of central tendency, if the data is symmetrical, the mean, median, and mode will coincide. However, when a large outlier is introduced, the mean will reflect this skew the most. The median will be the most appropriate measure of center for a data set with outliers since it is not affected by them. Therefore, adding a large number to a data set most significantly affects the mean, making it the correct option in the final part.