Question

The mean game scores and standard deviations of four seasons of a football team are given below. Season Mean Standard Deviation 2005 19 3.5 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.

Answer 1

Higher standard deviation shows a greater spread of the data. 

2005 - sd=3.5
2006 - sd=2.8
2007 - sd=1.0
2008 - sd=4.0

The correct statement is the last statement which says the game scores of season 2005 have a greater spread than the game scores of season 2006

Answer 2

Standard deviation shows the spread of data. The only correct option is the game scores of season 2005 have a greater spread than the game scores of season 2006.

What is the standard deviation?

A standard deviation is a difference in data points from the mean.

Given to us

2005  Mean-19 Standard deviation-3.5

2006  Mean-21 Standard deviation-2.8

2007  Mean-12 Standard deviation-1.0

2008  Mean-9 Standard deviation-4.0

We know that the standard deviation is the difference in the data points from the mean. therefore, if the data has a high standard deviation then the data points are more spread.

Now, arranging the data on the basis of its standard deviation,

2007 < 2006 < 2005 < 2008

Thus, Checking all the options, the only correct option is the game scores of season 2005 have a greater spread than the game scores of season 2006.

Learn more about Standard deviation:

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