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

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In summary: I think the median would be a better choice if there are no outliers, but with outliers the mean would be a better choice. I don't know how to justify it.Yes, the answers are reversed. I think the median would be a better choice if there are no outliers, but with outliers the mean would be a better choice. I don't know how to justify it.
  • #1
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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  • #2
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?
 
  • #3
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.
 
  • #4
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?
 
  • #5
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. :)
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 

What is the difference between mean and median?

The mean is the average of a set of values, calculated by adding all the values and dividing by the total number of values. The median is the middle value in a set of ordered values. If there is an even number of values, the median is the average of the two middle values.

When should I use mean instead of median?

Mean is generally used when the data is normally distributed, meaning the majority of values fall around the center with fewer values on the extremes. Median is used when the data is skewed, meaning there are a few extreme values that can affect the mean significantly.

Why is median sometimes preferred over mean?

Median is preferred over mean when there are outliers or extreme values in the dataset. These values can skew the mean and make it an inaccurate representation of the central tendency of the data. Median is less affected by outliers and provides a more robust measure of central tendency.

How do I calculate mean and median?

To calculate the mean, add all the values and divide by the total number of values. To calculate the median, first arrange the values in ascending order. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

Can I use mean and median together?

Yes, mean and median can be used together to get a better understanding of the data. If the mean and median are close in value, it suggests the data is normally distributed. If they are significantly different, it indicates the presence of outliers or a skewed distribution. Using both measures can provide a more comprehensive representation of the data.

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