Question

ty and gajge are both football players who averaged 4 yards per run in yesterday’s football game. the statistics from that game are shown in the table below.

player name	# of carries	average yards gained per run	longest run (yards)	shortest run (yards)
gajge	10	4.0	19	2

which statement best describes the data?

• the lengths of ty’s runs have greater variability because ty had more rushing attempts.
• the lengths of gajge’s runs have greater variability because there is a greater difference between his longest and shortest runs.
• ty’s and gajge’s runs have the same variability because they both average 4.0 yards per carry.
• ty’s and gajge’s runs have the same variability because they both had the same length shortest run.

Explanation:

Step1: Analyze Variability Concept

Variability in data can be assessed by the range (difference between maximum and minimum values) or other measures. Here, we check the range (longest - shortest run) for each player.
For Ty: Range = \( 6 - 2 = 4 \) yards.
For Gajge: Range = \( 19 - 2 = 17 \) yards.

Step2: Evaluate Each Option

• Option 1: Number of carries doesn't directly determine variability. Ty's range is smaller, so this is wrong.
• Option 2: Gajge's range (17) is greater than Ty's (4), so his runs have more variability. This matches the range analysis.
• Option 3: Same average doesn't mean same variability. Gajge's range is larger, so this is wrong.
• Option 4: Same shortest run doesn't mean same variability. Gajge's longest run is much larger, so range differs. This is wrong.

Answer:

The lengths of Gajge's runs have greater variability because there is a greater difference between his longest and shortest runs.