Question

ty and gage 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)
gage	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 gage’s runs have greater variability because there is a greater difference between his longest and shortest runs.
• ty’s and gage’s runs have the same variability because they both average 4.0 yards per carry.
• ty’s and gage’s runs have the same variability because they both had the same length shortest run.

Explanation:

Step1: Calculate the range for Ty and Gage

Range is a measure of variability. The formula for range is \(Range = Longest - Shortest\).
For Ty: \(Range_{Ty}=6 - 2=4\)
For Gage: \(Range_{Gage}=19 - 2 = 17\)

Step2: Analyze each option

• Option 1: Ty's runs have greater variability because Ty had more rushing attempts. Variability (e.g., range) is not about the number of attempts.
• Option 2: The lengths of Gage's runs have greater variability because there is a greater difference between his longest and shortest runs. Since \(Range_{Gage}(17)>Range_{Ty}(4)\), this is correct.
• Option 3: Ty's and Gage's runs have the same variability because they both average 4.0 yards per carry. Average (mean) is not the same as variability.
• Option 4: Ty's and Gage's runs have the same variability because they both had the same length shortest run. Shortest run alone does not determine variability.

Answer:

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