The mean is one type of middle value for a set of data. Another middle value is the median. You find the median of a set of data by listing the numbers in increasing order and finding the number halfway through the list.

Case 1: The set of numbers 6, 2, 7, 4, 11, 8, and 9 is first arranged in increasing order: 2, 4, 6, 7, 8, 9, 11

The median is the number halfway through the list, which is 7. Three numbers are below 7 and three numbers are above 7.

Case 2: If the number of terms in a list is even, split the difference between the two middle numbers. For instance, for the numbers 9, 3, 6, 2, 11, and 14, arrange them in increasing order: 2, 3, 6, 9, 11, 14

In this case, there are two middle numbers, 6 and 9. (There are two numbers below 6 and two above 9.) The median is the value halfway between 6 and 9, which is 7.5.

Case 3: If a number appears more than once in a list, keep that repetition and arrange the numbers in increasing order. For example, arrange the list 2, 8, 3, 2, 3, 6, and 7 in increasing order: 2, 2, 3, 3, 6, 7, 8

The “middle” number in this list is the “second” 3 (there are three items to its right and three to its left); so the median is 3.


1 Find the median for the Waiting for a Double data in the frequency bar graph. Explain using mathematical reasoning how you found it. You don’t have to write out all 300 numbers to do this.








2 Which number—the mean, the median, or perhaps something else—do you think best represents what happens when you “wait for a double”? Fully explain your thinking.