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 2008.
• 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 Standard Deviation Meaning

Standard deviation measures data spread. Larger value means greater spread.

Step2: Compare 2005 and 2006 SD

2005 SD: \( 3.5 \), 2006 SD: \( 2.8 \). Since \( 3.5 > 2.8 \), 2005 scores have greater spread than 2006.

Step3: Evaluate Other Options

• 2006 (2.8) vs 2008 (4.0): \( 2.8 < 4.0 \), so 2006 spread < 2008.
• 2007 (1.0) vs 2005 (3.5): \( 1.0 < 3.5 \), so 2007 spread < 2005.
• 2006 (2.8) vs 2005 (3.5): \( 2.8 < 3.5 \), so 2006 spread < 2005.

Answer:

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