median

[XINLAI-UE]

Hi,

"The data showed that respondents with the most positive attitudes survived a median of 22 years after their initial interview, "

I hope someone could have a look for me. I do not think I get this sentence exactly, does it mean - "Respondents with the most positives attitudes survived in the middle of 22 years (around 11 years) after their initial interview." Or " Around a half of these respondents (around 320 people) with the most positive attitudes survived 22 years after their initial interview." The word "median" here refers to the amount of the time or the respondents ?
What does this sentence mean?

Thanks for your help.



... The researchers found that people who view aging positively live longer than people who view it negatively. This study began 26 years go and took place in a small town in the Midwest. The participants were 640 men and women who were 50 to 90 years old at the the time. The subjects were asked to agree or disgree with statements about aging, like "As you get older, you become less useful" and "Older people can't learn new skills." The data showed that respondents with the most positive attitudes survived a median of 22 years after their initial interview, while those with negative views lives just 15 years - a difference of seven years.

[bhaisahab]

Originally Posted by XINLAI-UE

Hi,

"The data showed that respondents with the most positive attitudes survived a median of 22 years after their initial interview, "

I hope someone could have a look for me. I do not think I get this sentence exactly, does it mean - "Respondents with the most positives attitudes survived in the middle of 22 years (around 11 years) after their initial interview." Or " Around a half of these respondents (around 320 people) with the most positive attitudes survived 22 years after their initial interview." The word "median" here refers to the amount of the time or the respondents ?
What does this sentence mean?

Thanks for your help.



... The researchers found that people who view aging positively live longer than people who view it negatively. This study began 26 years go and took place in a small town in the Midwest. The participants were 640 men and women who were 50 to 90 years old at the the time. The subjects were asked to agree or disgree with statements about aging, like "As you get older, you become less useful" and "Older people can't learn new skills." The data showed that respondents with the most positive attitudes survived a median of 22 years after their initial interview, while those with negative views lives just 15 years - a difference of seven years.

It means that they survived an average of 22 years.

[Raymott]

Originally Posted by XINLAI-UE

... The researchers found that people who view aging positively live longer than people who view it negatively. This study began 26 years go and took place in a small town in the Midwest. The participants were 640 men and women who were 50 to 90 years old at the the time. The subjects were asked to agree or disgree with statements about aging, like "As you get older, you become less useful" and "Older people can't learn new skills." The data showed that respondents with the most positive attitudes survived a median of 22 years after their initial interview, while those with negative views lives just 15 years - a difference of seven years.

The "median" is one form of "average". More commonly, the "mean" is taken as the average.
The "mean" is all the values summed, then divided by the total number.
The "median" is the number such that 50% values are above and 50% below (approximately)
The median is often a better measure if there are extremes in the series.
For example, comparing incomes, here are five annual incomes for some teachers:
20,000; 25,000; 22,000; 23,000; 100,000.
The mean income is: 38,000
The median income is: 23,000
The median is a better indication of what people would call the "average" income.
The media often misuse these concepts, for example saying "The average income of teachers is 38,000. What are they complaining about?" But this is only because one teacher makes 100,000. They should say if they are quoting the mean or the median.

[XINLAI-UE]

[quote=Raymott;344783]The "median" is one form of "average". More commonly, the "mean" is taken as the average.
The "mean" is all the values summed, then divided by the total number.
The "median" is the number such that 50% values are above and 50% below (approximately)


Hi, Raymott,

Thanks for your reply.

I have a question. In this case, "median" can be taken as "average", but there is a little difference between them. I mean, more specifically, "median" refers to the middle value of these numbers, like you say:The "median" is the number such that 50% values are above and 50% below (approximately), so the median of these teachers' income is 23,000.

But "average" means the result of adding numbers together to find a total, and then dividing the total by the number of amounts, so the average of these teachers' income if 38,000.

So, "median" and "average" are a little different, and I think it is better for us to take "middle value" instead of taking "average" in this case. I mean, I should get this like, The data showed that respondents with the most positive attitudes survived a median (middle value) of 22 years after their initial interview.

Am I getting this in a correct right way?

In the end, there is a final question about your example.

For example, comparing incomes, here are five annual incomes for some teachers:
20,000; 25,000; 22,000; 23,000; 100,000.
The mean income is: 38,000
The median income is: 23,000 (How do you know the result of this one is 23,000? I did not work out what the method is, could you teach and tell me how to get the median of the numbers, thanks a lot!)

[Anglika]

So, "median" and "average" are a little different, and I think it is better for us to take "middle value" instead of taking "average" in this case. I mean, I should get this like, The data showed that respondents with the most positive attitudes survived a median (middle value) of 22 years after their initial interview.

Am I getting this correct?

incomes for some teachers:
20,000; 25,000; 22,000; 23,000; 100,000.
The mean income is: 38,000
The median income is: 23,000 (How do you know the result of this one is 23,000? I did not work out what the method is, could you teach and tell me how to get the median of the numbers, thanks a lot!) You remove the lowest and the highest figures [20K and 100K], add the remaining figures together and divide by the number of sums involved.

[Raymott]

Originally Posted by Anglika

You remove the lowest and the highest figures [20K and 100K], add the remaining figures together and divide by the number of sums involved.

Well, no. That just gives you another mean without the first and last values.
Generally, to get the median (these days) you put all your values in Excel or another spreadsheet, sort them, count them (n = 5) and take the ((n+1)/2)th value (3) (the middle value). You don't need to remove any.

[Raymott]

20,000; 25,000; 22,000; 23,000; 100,000.
The mean income is: 38,000
The median income is: 23,000 (How do you know the result of this one is 23,000? I did not work out what the method is, could you teach and tell me how to get the median of the numbers, thanks a lot!)

Or you could do it Anglika's way (some computers probably use this algorithm). But you have to keep taking values away.

Input: array of values. Ouput: median
Until the number of values is 2 or fewer {
.... Remove the highest value;
.... Remove the lowest value;
} // This loops until 1 or 2 values remain
If one value remains, return that value as median
else if 2 values remain, return (val1+val2)/2 as median.
Stop.

[XINLAI-UE]

Originally Posted by Raymott

Well, no. That just gives you another mean without the first and last values.
Generally, to get the median (these days) you put all your values in Excel or another spreadsheet, sort them, count them (n = 5) and take the ((n+1)/2)th value (3) (the middle value). You don't need to remove any.

Hello, Raymott,

It is good to see you, thank you.

"count them (n = 5) and take the ((n+1)/2)th value (3) (the middle value). "

I do not get this one, so I was wondering if you could offer me some explanation with one example, may be we can take the Teacher's Income as one, do we ?

[Raymott]

Originally Posted by XINLAI-UE

Hello, Raymott,

It is good to see you, thank you.

"count them (n = 5) and take the ((n+1)/2)th value (3) (the middle value). "

I do not get this one, so I was wondering if you could offer me some explanation with one example, may be we can take the Teacher's Income as one, do we ?

Um, that was an example of the teachers income.
Here they are sorted from smallest to largest:
20,000; 22,000; 23,000; 25,000; 100,000.

There were 5 values. n= 5. (5+1)/2 = 3, so you take the third value
The third value is 23,000.
If you start with an even number, say 6, you'll get 3.5 (6+1)/2 = 7/2 = 3.5. In this case, you average the 3rd and 4th values (3rd value + 4th value) / 2.
If you have 1000 values, you take the 1001/2 = 500.5th, which the (500th + 501st) / 2.

[XINLAI-UE]

Originally Posted by Raymott

Um, that was an example of the teachers income.
Here they are sorted from smallest to largest:
20,000; 22,000; 23,000; 25,000; 100,000.

There were 5 values. n= 5. (5+1)/2 = 3, so you take the third value
The third value is 23,000.
If you start with an even number, say 6, you'll get 3.5 (6+1)/2 = 7/2 = 3.5. In this case, you average the 3rd and 4th values (3rd value + 4th value) / 2.
If you have 1000 values, you take the 1001/2 = 500.5th, which the (500th + 501st) / 2.

Hello, Raymott,

Yes, I get it. I also find answer here: Mean, Median, Mode, and Range
It is interesting. It seems I learn a lot of another knowledges from you besides Engish !

Thank you very much!