A small startup has 10 employees including the founders.....

eddy2017

eddy2017

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Which values in the above table are outliers? Should you trim the values from both ends? Compute the trimmed mean by removing only the outliers and not necessarily by trimming values from both ends.
 
mean salary =
(90+80+18+18+17+16+16+16+15+14) / 10 = (300/10)
mean salary = 30
is the mean salary the right measure. If not why?
well, I have read the mean is impacted by outliers. I think I can consider 90 and 80 outliers here.
So, it is not the right measurement of central tendency to be used here.

Should you trim the values from both ends? Compute the trimmed mean by removing only the outliers and not necessarily by trimming values from both ends.
I am stuck here, what does that mean?
 
  • A trimmed mean removes a small designated percentage of the largest and smallest values before calculating the average.
  • Using a trimmed mean helps eliminate the influence of outliers or data points on the tails that may unfairly affect the traditional mean. (from Investopedia)
    how can I do the trimming?. Any hint or video to watch?

I am watching a couple of tutorials on how to trim means. So, give me some time and I will attempt a response.
 
eddy2017 said:
  • A trimmed mean removes a small designated percentage of the largest and smallest values before calculating the average.
  • Using a trimmed mean helps eliminate the influence of outliers or data points on the tails that may unfairly affect the traditional mean. (from Investopedia)
    how can I do the trimming?. Any hint or video to watch?

I am watching a couple of tutorials on how to trim means. So, give me some time and I will attempt a response.
Click to expand...
Calculate the MEDIAN of the data set. What do you get?
 
I add up al the terms of the data set and divide the result by the total number of terms in the data set
sum= 300/3
=30
 
median
arranging all numbers from least to greatest
90+80+18+18+17+16+16+16+15+14
14,15,16 ,16,16,17,18,18, 80,90

find the middle number
middle numbers=16,17
Adding them up =33 /2
median=16.5
 
Subhotosh Khan said:
I shouted MEDIAN......

Now tell us what did you learn about trimmed mean and how are those calculated.
Click to expand...
we trim means when there are outliers that are skewing the data distribution.
we find the untrimmed mean first
adding up all data and dividing it by the number of terms in the data set

now we trim from both ends of the data set and then we take a look at the outliers on the upper and lower end.
the tutorial that I watched said that there is always a percent to be trimmed, like they ask you to find the 20 % of the trimmed mean
it is not the case here, so this is all I can tell you, as in,
Suppose the problem asks you to find 20% of the reduced mean
and we have 25 terms in the data set
20% of 25 =5
Then we remove 5 values starting at both ends of the distribution(already arranged from least to greatest)
and then we proceed to get the reduced mean as we do a normal mean.
but i this case the problem doesn't ask me for a percent to be trimmed. So, I am in doubt about how to go on.
the tutor goes on to even give a formula to find the amount of numbers to be reduced

1645728595020.png

Numbers that are deleted from both ends = trimming % * the number of data in the data set
 
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and then summin' it up, we can see that the trimmed mean is a lot less without the outliers and that is the whole point of trimming off a distribution with outliers

Subhotosh Khan said:
I shouted MEDIAN......

Now tell us what did you learn about trimmed mean and how are those calculate
Click to expand...
 
Eddy

I am not going to interfere with SK's assistance on mechanics. What I will ask is what does the question whether the mean is the right measure even mean?
 
but taking a look at this data set the outliers are on one end only, not both ends of the data set, the salary values 80 and 90 in the above data are outliers., but I am not seeing any more extreme values on the other end,
so my question is: should I trim the outliers on that side and then re-compute the mean but now without the outliers?. if so, then I know the solution

JeffM said:
Eddy

I am not going to interfere with SK's assistance on mechanics. What I will ask is what does the question whether the mean is the right measure even mean?
Click to expand...
Jeff, I suppose they can ask me that because the mean is not very amenable to outliers, then they expect me to say, yes, but it needs to be trimmed.
because if they want me to say no, it is not the right measure, so there is no logic to their final question:
Compute the trimmed mean by removing only the outliers and not necessarily by trimming values from both ends.

eddy2017 said:
Jeff, I suppose they can ask me that because the mean is not very amenable to outliers, then they expect me to say, yes, but it needs to be trimmed.
because if they want me to say no, it is not the right measure, so there is no logic to their final question:
Compute the trimmed mean by removing only the outliers and not necessarily by trimming values from both ends.
Click to expand...
I agree it is kind a dum question to ask.

eddy2017 said:
I agree it is kind a dum question to ask.
Click to expand...
but it is grist to my mill anyways because I have never heard about trimming the mean so it is a good one for me.
 
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Eddy

Here is my point.

If I want to know what the payroll of the company is, the mean is the right measure.

If I want to know what most people make in the company, the median, the mode, or a trimmed mean are all equally good.

You cannot tell which is a good measure until you know what its purpose is.
 
That is good information. Thanks.

JeffM said:
Eddy

Here is my point.

If I want to know what the payroll of the company is, the mean is the right measure.

If I want to know what most people make in the company, the median, the mode, or a trimmed mean are all equally good.

You cannot tell which is a good measure until you know what its purpose is.
Click to expand...
I know what you mean, but let me tell you that there are many stupid questions around when it comes to math. teachers throw stuff around for students to answer without much thought. Not at least with the thought and logical thinking you put into them.
I had this very same question (a version of this question) in my first math test. I failed it. (of course, I was not a member of this forum yet). The one I posted now with a histogram is a very common question in testing statistics. So, what I mean, Jeff, is that as long as a question makes me look for formula and makes me apply it and demands at least a method to do something it is good for me at least for practice.
 
eddy2017 said:
median
arranging all numbers from least to greatest
90+80+18+18+17+16+16+16+15+14
14,15,16 ,16,16,17,18,18, 80,90

find the middle number
middle numbers=16,17
Adding them up =33 /2
median=16.5
Click to expand...
Do you really think that the middle number or numbers be different if you go from lowest to highest vs highest to lowest? If yes, then you need to learn what the middle means.
 
Steven G said:
Do you really think that the middle number or numbers be different if you go from lowest to highest vs highest to lowest? If yes, then you need to learn what the middle means.
Click to expand...
I was taught yhat to find the median of a data set you need to arrange the data points from smallest to largest.
Is that correct or not?
 
If you believe that you must arrange the data from smallest to largest to find the median then you are greatly mistaken.

The middle number (or numbers) have the same number of numbers to the left and right of this middle number. Look at any list and check for yourself if you must go from smallest to largest vs largest to smallest.

If you teacher said that you must go from smallest to largest, then your teacher was wrong. If you teacher said since you can go from smallest to largest OR from largest to smallest, we'll choose in our class to go from smallest to largest--your teacher was perfect correct in saying that.
 
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