Which measure of center is most accurate for the batting averages of a team?

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SUMMARY

The discussion centers on determining the most accurate measure of center for two datasets: rainfall and batting averages. For the rainfall data, which contains outliers, the median is recommended as the best measure of center due to its resistance to extreme values. Conversely, for the batting averages of the team, the mean is deemed appropriate as it effectively summarizes the players' overall performance. The guidelines suggest using the mean for similar values and the median for datasets with outliers, although the participants noted a reversal in their application.

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rebo1984
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The rainfall (in inches) in the month of June for 7 years is recorded below.
20, 24, 53, 13,0, 43, 36
What is the best measure of center ?The batting averages of 10 players of a team are
0.338, 0.234, 0.256, 0.321, 0.333, 0.290, 0.148, 0.222, 0.300, 0.276
What is the best measure of center ?

Please help/explain.
 
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Hello rebo1984 and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
greg1313 said:
Hello rebo1984 and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

I'm not sure what the answer is. Since the first one has outliers, I thought the median would be the better choice. The second one I think can be done using the mean. I am not sure, looking for an explanation.
 
rebo1984 said:
i'm not sure what the answer is. Since the first one has outliers, i thought the median would be the better choice. The second one i think can be done using the mean. I am not sure, looking for an explanation.

could someone please help?
 
rebo1984 said:
could someone please help?

Hi rebo1984,

What rules and guidelines have you been given to decide? In general I agree with your answers. The median is less sensitive to outliers and given the spread of the data is set 1 that makes sense. In set 2 I think the mean would nicely capture the team's batting average as the (# of hits for all 10 players)/(# times at bat for all 10 players). This nicely summarizes the team's actual performance with these 10 players. So overall I agree with your post, but knowing how you are supposed to justify these could be helpful. :)
 
Jameson said:
Hi rebo1984,

What rules and guidelines have you been given to decide? In general I agree with your answers. The median is less sensitive to outliers and given the spread of the data is set 1 that makes sense. In set 2 I think the mean would nicely capture the team's batting average as the (# of hits for all 10 players)/(# times at bat for all 10 players). This nicely summarizes the team's actual performance with these 10 players. So overall I agree with your post, but knowing how you are supposed to justify these could be helpful. :)

The guidelines state that the mean should be used if the values are similar, and that the median should be used if there are outliers, yet the answers are reversed.So I'm confused.
 
rebo1984 said:
The guidelines state that the mean should be used if the values are similar, and that the median should be used if there are outliers, yet the answers are reversed.So I'm confused.

Yes, those are typically how these two metrics for the center of the data are used. So it comes down to how do we define "having outliers"? In real life this becomes a little bit subjective, but often we can say we look at the mean and points lie outside of 3-4 standard deviations from the mean, then there are outliers. In beginning statistics courses, usually it's more of an eyeball cutoff. How have you over outliers? Are you saying that you have heard the answers to these should be reversed?
 
Jameson said:
Yes, those are typically how these two metrics for the center of the data are used. So it comes down to how do we define "having outliers"? In real life this becomes a little bit subjective, but often we can say we look at the mean and points lie outside of 3-4 standard deviations from the mean, then there are outliers. In beginning statistics courses, usually it's more of an eyeball cutoff. How have you over outliers? Are you saying that you have heard the answers to these should be reversed?

Yes, the answers are reversed.