If a data set gains new values, which statistics can change?

• A. Only the mode
• B. Only the median
• C. The mean, median, mode, and range
• D. None of the measures change

Answer: (C)

Adding new values to a data set can change each of these measures because they summarize the data in different ways.

The mean uses every number in the set, so when you add another value, both the total sum and the count change, which can push the average up or down. For example, with 2, 4, 6 the mean is 4; adding a 10 changes the mean to 5.5.

The median is the middle value once all numbers are sorted. Adding values can shift which number sits in the middle, especially if you add numbers smaller than the current minimum or larger than the current maximum. For instance, with 1, 2, 9 the median is 2; adding 0 gives 0, 1, 2, 9 and the median becomes 1.5.

The mode is the most frequent value. If the new values make a different number occur more often than the current mode, or create a new value that ties or wins, the mode can change. You could, for example, add many copies of a new number so that it becomes the most frequent.

The range is the difference between the maximum and minimum. A new value outside the current range can widen it (or a new value that’s inside the range won’t change it). For example, starting with 2 and 7 gives a range of 5; adding 12 increases the range to 10.

So, when a data set gains new values, the mean, median, mode, and range all have the potential to change depending on what those new values are.