A mean gives you a total: multiply it by the number of values, then use that total to find the missing observation. To find the median, put every value in order and locate the middle. With an even number of values, average the two middle values. Don’t report the given mean when the question asks for the median.
Hints
- Hint 1
The mean is the total divided by the number of times. Work backward: what total must eight times have if their mean is minutes?
- Hint 2
The seven known times account for part of that total. Use a Desmos regression to find the missing time , then put it in the list where it belongs.
- Hint 3
The median comes from positions in the ordered list, not from its total. With eight times, which values occupy the fourth and fifth positions?
Step-by-step
Find the missing time, then the middle
Step 1Turn the mean into a total
The mean is the total divided by the number of times. So a mean of minutes for eight hikers means their times add to :
- Step 2
Find the missing time in Desmos
Type to store the known times. Then type . The tells Desmos to find the unknown that makes the totals match. Under PARAMETERS, Desmos shows , so the missing time is minutes.
- Step 3
Locate the two middle times
Put the missing after to order all eight times:
For eight ordered values, the median lies halfway between the fourth and fifth. Those times are and . The given mean of doesn’t tell you the median.
- Step 4
Average the middle times
Type in Desmos. It shows , so the median completion time is minutes. Choice C.