A median is the middle value after the observations are ordered. In a table of employee-count ranges, count how many restaurants each row covers until you reach the middle restaurant. Don't pick the middle table row: rows can contain different numbers of restaurants, and the exact employee counts within each range aren't given.
Hints
- Hint 1
For an odd number of observations, the median has the same number of observations on either side. With restaurants, how many come before the middle restaurant, and which position is it?
- Hint 2
A frequency tells you how many restaurants are in a range. Count through the ranges from smallest to largest to find which one contains the middle restaurant. Then ask whether a choice could be a count within that range.
Step-by-step
Count to the middle restaurant
Step 1Find the middle position
No Desmos needed. The table's counts let you locate the middle restaurant directly. The median is the middle employee count when the restaurants are ordered from fewest employees to most. With restaurants, eight come before and eight come after the middle one, so you need the ninth restaurant.
- Step 2
Count through the ranges
The first restaurants occupy positions and . The next occupy positions through , and the following occupy positions and . So the ninth restaurant is in the -to- row, not the middle row of the table. Count restaurants, not rows, to locate a median.
- Step 3
Check what the middle count could be
The ninth restaurant can have any employee count from to , including . For example, all restaurants in that row could have employees and still fit the table. So the median could be employees. Choice D.