Question

the mean game scores and standard deviations of four seasons of a football team are given below.

season	mean	standard deviation
2006	21	2.8
2007	12	1.0
2008	9	4.0

which statement must be true?

• the game scores of season 2006 have a greater spread than the game scores of season 2005
• the game scores of season 2007 have a greater spread than the game scores of season 2005.
• the game scores of season 2006 have a greater spread than the game scores of season 2005.
• the game scores of season 2005 have a greater spread than the game scores of season 2006.

Explanation:

Step1: Recall Spread and Standard Deviation

Spread in data is related to standard deviation; higher standard deviation means greater spread.

Step2: Compare 2005 and 2006 Std Dev

2005 std dev: \( 3.5 \), 2006 std dev: \( 2.8 \). Since \( 3.5 > 2.8 \), 2005 has greater spread than 2006.

Step3: Evaluate Other Options

• 2007 std dev (\( 1.0 \)) < 2005 (\( 3.5 \)): so 2007 spread < 2005.
• 2006 std dev (\( 2.8 \)) < 2005 (\( 3.5 \)): so 2006 spread < 2005.

Answer:

The game scores of season 2005 have a greater spread than the game scores of season 2006.