Question

In the fall semester of 2009, the average Graduate Management Admission Test (GMAT) of the students at a certain university was 500 with a standard deviation of 90. In the fall of 2010, the average GMAT was 570 with a standard deviation of 85.5. Which year's GMAT scores show a more dispersed distribution

Answer 1

Answer:

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

Step-by-step explanation:

To verify how dispersed a distribution is, we find it's coefficient of variation.

Coefficient of variation:

Mean of $\mu$, standard deviation of $\sigma$. The coefficient is:

$CV = \frac{\sigma}{\mu}$

Which year's GMAT scores show a more dispersed distribution

Whichever year has the highest coefficient.

2009:

Mean of 500, standard deviation of 90. So

$CV = \frac{90}{500} = 0.18$

2010:

Mean of 570, standard deviation of 85.5. So

$CV = \frac{85.5}{570} = 0.15$

Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution

Answer 2

2009's GMAT scores show a more dispersed distribution.

Given that in 2009: Mean = 500 and standard deviation = 90.

In 2010: Mean = 570 and standard deviation = 85.5.

If the standard deviation is higher then the scores will be more dispersed.

Note that: 90 > 85.5. And 90 corresponds to 2009.

So, 2009's GMAT scores show a more dispersed distribution.

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