Question

the following tables give information about the weekly number of hamburgers sold at two outlets of the fatzzo hamburger house.

franchise x
minimum hamburgers 468
lower quartile 495
median 519
upper quartile 543
maximum hamburgers 612

franchise y
minimum hamburgers 591
lower quartile 644
median 672
upper quartile 705
maximum hamburgers 770

select the 2 statements that are true about the number of hamburgers sold at each franchise.

1. franchise y always sells more than franchise x.
2. the number of burgers sold by franchise x is increasing weekly.
3. at least 75% of the time franchise y sells more than franchise x.
4. the range of franchise y is greater than the range of franchise x.

options:
2 and 4 only
1 and 2 only
1 and 3 only
2 and 3 only
3 and 4 only

Explanation:

Step1: Analyze Statement 1

Franchise X's maximum is 612, Franchise Y's minimum is 591. So X can sell more than Y (e.g., X=612, Y=591). Thus, Statement 1 is false.

Step2: Analyze Statement 2

The table gives summary stats (min, Q1, median, Q3, max), not weekly trends. No info on weekly increase. So Statement 2 is false.

Step3: Analyze Statement 3

Franchise Y's lower quartile (644) is greater than Franchise X's upper quartile (543). So at least 75% (Q1 to max) of Y's data is above X's Q3, meaning at least 75% of the time Y sells more. Statement 3 is true.

Step4: Analyze Statement 4

Range of X: \( 612 - 468 = 144 \). Range of Y: \( 770 - 591 = 179 \). \( 179 > 144 \), so Y's range is greater. Statement 4 is true.

Answer:

3 and 4 only