Pregunta
Based on these facts, would you expect batting averages above .350 to be more or less common today than in the past?
A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation
is lower, thus it is less probable to have such a high batting average.
B. Because the mean is unchanged, batting averages above .350 are more common today because the standard deviation
is higher, thus it is less probable to have such a high batting average.
C. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation
is higher, thus it is more probable to have such a high batting average.
D. Because the mean is unchanged, batting averages above 350 are more common today because the standard deviation
is lower, thus it is less probable to have such a high batting average.
A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation
is lower, thus it is less probable to have such a high batting average.
B. Because the mean is unchanged, batting averages above .350 are more common today because the standard deviation
is higher, thus it is less probable to have such a high batting average.
C. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation
is higher, thus it is more probable to have such a high batting average.
D. Because the mean is unchanged, batting averages above 350 are more common today because the standard deviation
is lower, thus it is less probable to have such a high batting average.
Ask by Macdonald Reed. in the United States
Jan 22,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Batting averages above .350 are less common today because the standard deviation is lower, making high averages less probable.
Solución
To analyze the question regarding batting averages above .350, we need to consider the relationship between the mean, standard deviation, and the distribution of batting averages.
- Mean: The average batting average remains unchanged.
- Standard Deviation: This measures the spread of the batting averages around the mean.
Now, let’s evaluate the options:
-
Option A: This states that batting averages above .350 are less common today because the standard deviation is lower. This is correct because a lower standard deviation means that the data points (batting averages) are closer to the mean, making it less likely to have values significantly above the mean, such as .350.
-
Option B: This suggests that batting averages above .350 are more common today because the standard deviation is higher. This is incorrect because a higher standard deviation would mean a wider spread of values, but since the mean is unchanged, it does not imply that values above .350 are more common.
-
Option C: This states that batting averages above .350 are less common today because the standard deviation is higher. This is contradictory because a higher standard deviation would actually allow for more values above the mean, making it more likely to have high averages.
-
Option D: This suggests that batting averages above .350 are more common today because the standard deviation is lower. This is incorrect for the same reason as option A; a lower standard deviation would make high averages less common.
Based on this analysis, the correct answer is:
A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is lower, thus it is less probable to have such a high batting average.
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Simplifique esta solución Bonus Knowledge
In the realm of baseball statistics, batting averages are influenced by various factors, including player skill, pitching quality, and even the type of ball being used. Historically, we saw peaks in batting averages during different eras, but as training, analytics, and game strategies have evolved, we’ve seen shifts in performance metrics. The lower standard deviations in recent years suggest that the top players are more consistently excellent, making those lofty averages rarer.
So, if the mean hasn’t changed while the standard deviation has decreased, it indeed makes it statistically less likely for players to reach those elite .350 averages, as they have less room to diverge from that central average. In essence, today’s baseball landscape has shaped a new normal for batting averages!
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