For a mean-versus-median comparison, first find the middle value of each ordered list. The mean uses every value, while the median depends on position. An unusually high value can raise the mean without moving the median. Rule out balanced lists, then use a Desmos list to check the remaining means. Watch the sign of an extreme value: a large negative number pulls the mean down.
Hints
- Hint 1
Each list has five values in order. The median is the third value, with two values on either side. What is that value in each list?
- Hint 2
A mean is the total divided by the number of values. If every value is the same, or values pair up evenly around the middle, can the mean be greater than the median?
- Hint 3
The remaining lists have an extreme value at one end. Enter each as a Desmos list and find its mean. Does the negative extreme pull the mean above or below its median?
Step-by-step
Read the middles, then check the means
Step 1Find each median
Each list is already in order and has five values, so its median is the third value. In the order shown, the medians are , , , and .
- Step 2
Rule out the balanced lists
Five s have a mean of , equal to their median. In , the negative and positive values cancel in pairs, so the mean is , also equal to its median. Equal doesn't meet “less than.”
- Step 3
Check the list with the negative extreme
Type , then . Desmos shows . That's below this list's median, , so the list has the comparison backward.
- Step 4
Check the list with the positive extreme
Type , then . Desmos shows . The lifts the mean, but the median stays at the third value, . Since , this data set has a median less than its mean. Choice C.