The median is the middle value after the data are sorted. When a question gives ranges and counts instead of individual values, find the middle position, then count through the ranges until you reach it. Desmos can check the arithmetic. Don't treat a range boundary as the median: the values within a range aren't specified.
Hints
- Hint 1
An odd number of values has one middle position when sorted. For 37 shops, find that position by adding 1 to 37 and dividing by 2.
- Hint 2
Each range fills a stretch of positions in the ordered list. Count the seven shops in the lowest range first, then the 19 shops in the next range. Which stretch contains the middle position?
- Hint 3
A range tells you the limits, not the exact count for each shop in it. Once you've located the middle shop's range, check which suggested count could belong to that shop.
Step-by-step
Count to the middle shop
Step 1Find the middle position
The median is the middle count after all 37 counts are ordered. With an odd number of values, its position is . Type in Desmos; it shows . So you need the 19th shop, not the 19th customer.
- Step 2
Place the lowest-count shops
The seven shops serving fewer than customers come first when the counts are ordered. They fill positions through , so the next range begins at position .
- Step 3
Find where the next range ends
Type on the next Desmos line; it shows . So the next 19 shops fill positions through . Position is in that stretch. Locate the median by its position, not by a range boundary.
- Step 4
Choose a possible count
The 19th shop served at least but fewer than customers. Its exact count isn't given, so it could have served customers. That makes a possible median daily customer count. Choice B.