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English to English translations [PRO] Science / statistical data 

English term or phrase: mean/average  In English there seem to be a difference between 'average' en 'mean' in statistical data. Can anybody explain me this difference?
Ex.
Mean age of the patients, average age of the patients. 
  NO DIFFERENCE  Explanation: mean3 something halfway between two extremes. [3 more definition(s)]
Syllables: mean
Parts of speech: noun , adjective
Part of Speech noun
Pronunciation min
Definition 1. something halfway between two extremes.
Synonyms average (1)
Similar Words normal , norm , median , par
Definition 2. the average number or amount, usu. calculated by adding all the values in a distribution and dividing their sum by the number of such values.
Synonyms arithmetic mean , average (2)
Crossref. Syn. average
Definition 3. moderation.
Example the ideal of the golden mean.
Synonyms moderation (1)
Similar Words golden mean , restraint
Related Words mode , middle , compromise
Part of Speech adjective
Definition 1. being between extremes, esp. in the middle; intermediate.
Synonyms intermediate , moderate (3) , medium , median (1) , middle (1,2)
Crossref. Syn. average
Similar Words normal , average , middling , OK , ordinary
Related Words medium , temperate , middle
Syllables: arithmetic mean
Part of Speech noun
Pronunciation ae rihth meh tihk min
Definition 1. the sum of a series of quantities divided by the number of quantities; average.
Crossref. Syn. mean , average
Definition 2. the arithmetic mean gained by adding two or more quantities and then dividing by the total number of quantities.
Example The average of four and six and two is four.
Synonyms mean3 (2) , arithmetic mean
Definition 3. any of several other arithmetic products, such as a median or a batting average.
Synonyms mean3 (2)
Similar Words statistics , figures , totals , median
 Note added at 20020706 10:59:16 (GMT) 
Syllables: average
Parts of speech: noun , adjective , transitive verb , intransitive verb
Phrases: average out , on the average
Part of Speech noun
Pronunciation ae vE rihj
aev rihj
Definition 1. a usual amount or kind; that which is not extreme or extraordinary.
Synonyms standard (2) , norm (1)
Crossref. Syn. normal , mean
Similar Words normal , rule , usual , par
Definition 2. the arithmetic mean gained by adding two or more quantities and then dividing by the total number of quantities.
Example The average of four and six and two is four.
Synonyms mean3 (2) , arithmetic mean
Definition 3. any of several other arithmetic products, such as a median or a batting average.
Synonyms mean3 (2)
Similar Words statistics , figures , totals , median
Related Words ordinary
Phrase on the average
Part of Speech adjective
Definition 1. usual or typical; not extreme.
Synonyms normal (1) , typical (2)
Crossref. Syn. passable , temperate
Similar Words mediocre , common , usual , runofthemill , middling , moderate , standard , indifferent , soso , par , ordinary , gardenvariety , four
Definition 2. obtained by determining the arithmetic mean, in which the sum of the quantities is divided by the total number of quantities.
Example the average daily rainfall.
Synonyms mean3
Related Words mild , mean , simple , routine , medium , adequate , modest
Part of Speech transitive verb
Inflected Forms averaged, averaging, averages
Definition 1. to find the arithmetic mean of (a set of quantities).
Definition 2. to achieve as a typical amount.
Example He averaged six miles a day when running ; He averaged ten dollars a day in tips.
Similar Words total , achieve
Part of Speech intransitive verb
Definition 1. to be or achieve an average.
Phrase average out
 Note added at 20020706 11:40:29 (GMT) 
In statistics, given a list of numbers, the mean is the number which is in the middle whereas the average or arithmetic mean is the number obtained when adding up the values represented by each item on the list and then dividing by the total number of items.
LIST: 1,2,4,5,6
Mean=4
Arithmetic Mean/Average = ((1+2+4+5+6)/5)=18/5=3 3/5
 Note added at 20020706 11:45:57 (GMT) 
If there are an even number of items in the list, the mean is the average of the two middle items. For example, if there are 6 items, let\'s say I lengthen this list by adding the number 7 for a list of an even number of items (6), the mean is 4.5. (The sum of 4 and 5 added together and divided by 2). The average will be calculated by adding the number 7 to the numerator and the denominator in this case is 6 rather than 5. LIST: 1,2,4,5,6,7
Mean = 4.5 = (4+5)/2 (Halfway between the third and fourth items)
Arithmetic Mean/Average = ((1+2+4+5+6+7)/5) = 25/5 = 5
 Note added at 20020706 18:41:55 (GMT) 
arithmetic mean
See mean (cf Mean, Median and Mode Discussion).
average
It is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted means, among other things (cf Mean, Median and Mode Discussion). mean
The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean (cf Mean, Median and Mode Discussion).
median
\"Middle value\" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50% (cf Mean, Median and Mode Discussion).
Mean, Median, and Mode Discussion
Student: When do we use mean and when do we use median?
Mentor: It is up to the researcher to decide. The important thing is to make sure you tell which method you use. Unfortunately, too often people call mean, median and mode by the same name: average.
Student: What is mode?
Mentor: The easiest way to look at modes is on histograms. Let us imagine a histogram with the smallest possible class intervals (see also Increase or Decrease? Discussion).
Student: Then every different piece of data contributes to only one bin in the histogram.
Mentor: Now let us consider the value that repeats most often. It will look like the highest peak on our histogram. This value is called the mode. If there are several modes, data is called multimodal. Can you make an example of trimodal data?
Student: Data with three modes? Sure. Say, if somebody counted numbers of eggs in 20 tree creeper\'s nests, they could get these numbers: 4, 3, 1, 2, 6, 3, 4, 5, 2, 6, 4, 3, 3, 3, 6, 4, 6, 4, 2, 6. I can make a histogram:
Mentor: There are three values that appear most often: 3, 4, and 6, so all these values are modes. Modes are often used for socalled qualitative data, that is, data that describes qualities rather than quantities.
Student: What about median?
Mentor: Median is simply the middle piece of data, after you have sorted data from the smallest to the largest. In your nest example, you sort the numbers first: 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6 eggs. There is an even number of values, so the middle (or median) is between the first and second 4. Because they are the same, we can easily say that the median is four, but if they were different, say if the median was between a 3 and a 4, we would do (3+4)/2=3.5.
Student: So, if there is an even number of values, the median is equal to the sum of the two middle values divided by two.
Mentor: If no birds had nests with only one egg, we would have values of 2, 3, 4, 5, and 6. In this case, the middle number or the median would be the second 4, and we would not need to add or divide because there were an odd number of values.
Student: The last type of averages I would like to know about is mean.
Mentor: Sometimes it is called arithmetic mean, because there are other things in math that are called mean. For example, there is a geometric mean and a harmonic mean. The arithmetic mean of a set of values is a sum of all values, divided by their number. In your nest example,
mean = (4+3+1+2+6+3+4+5+2+6+4+3+3+3+6+4+6+4+2+6)/20 = 3.65
Student: Which one is better: mean, median or mode?
Mentor: It depends on your goals. I can give you some examples to show you why. Consider a company that has nine employees with salaries of 35,000 a year, and their supervisor makes 150,000 a year. If you want to describe the typical salary in the company, which statistics will you use?
Student: I will use mode (35,000), because it tells what salary most people get.
Mentor: What if you are a recruiting officer for the company that wants to make a good impression on a prospective employee?
Student: The mean is (35,000*9 + 150,000)/10 = 46,500 I would probably say: \"The average salary in our company is 46,500\" using mean.
Mentor: In each case, you have to decide for yourself which statistics to use.
Student: It also helps to know which ones other people are using!
I\'m going to wait to talk about range for a moment and concentrate on
mean, median, and mode. Mean, median, and mode are all types of
averages, although the mean is the most common type of average and
usually refers to the _arithmetic mean_ (There are other kinds of means
that are more difficult).
The arithmetic mean is a simple type of average. Suppose you want to
know what your numerical average is in your math class. Let\'s say your
grades so far are 80, 90, 92, and 78 on the four quizzes you have had.
To find your quiz average, add up the four grades:
80 + 90 + 92 + 78 = 340
Then divide that answer by the number of grades that you started with,
four: 340 / 4 = 85. So, your quiz average is 85! Whenever you want to
find a mean, just add up all the numbers and divide by however many
numbers you started with.
But sometimes the arithmetic mean doesn\'t give you all the information
you want, and here is where your first and third questions come in.
Suppose you are an adult looking for a job. You interview with a
company that has ten employees, and the interviewer tells you that the
average salary is $200 per day. Wow, that\'s a lot of money! But that\'s
not what you would be making. For this particular company, you would
make half of that. Each employee makes $100 per day, except for the
owner, who makes $1100 per day. What? How do they get $200 for average
then?!
Well, let\'s take a look:
Nine employees make $100, so adding those up is 9 x 100 = 900. Then
the owner makes $1100, so the total is $1100 + $900 = $2000. Divide by
the total number of employees, ten, and we have $2000/10 = $200.
Because the owner makes so much more than everyone else, her salary
\"pulls\" the average up.
A better question to ask is, \"What is the _median_ salary?\" The median
is the number in the middle, when the numbers are listed in order. For
example, suppose you wanted to find the median of the numbers 6, 4,
67, 23, 6, 98, 8, 16, 37. First, list them in order: 4, 6, 6, 8, 16,
23, 37, 67, 98. Now, which one is in the middle? Well, there are nine
numbers, so the middle one is the fifth, which is 16, so 16 is the
median.
Now, what about when there is an even number of numbers? Look at the
quiz grade example again: 90, 80, 92, 78. First list the numbers in
order: 78, 80, 90, 92. The two middle ones are 80 and 90. So do we have
two medians? No, we find the mean of those two: 80 + 90 = 170, and
170 / 2 = 85. So 85 is the median (and in this case the same as the
mean)!
Now look at those salaries again. To find the median salary, we look at
the salaries in order: 100, 100, 100, 100, 100, 100, 100, 100, 100,
1100. This is an even number of salaries, so we look at the middle
two. They are both 100, so the median is $100. That\'s much better at
telling you how much you\'ll make if you accept the job.
But the median doesn\'t always give you the best information either.
Suppose you interview with a company that has 10 general employees, 7
assistants, 3 managers, and 1 owner. For this company, the mean salary
is $400, and the median is also $400. But you are applying for the
position of general employee, whose starting salary is $100! Why are
the mean and median so far away?
Well, the 10 general employees each make $100. The 7 assistants each
make $400, the 3 managers each make $900, and the owner makes $1900.
If you do the math to find the median or mean, $400 is the answer (try
it!). So what can you do?
The mode is the type of average you want to know in this situation.
The mode is the number the occurs most frequently. In the example for
median, 6 would be the mode because it occurs twice, while the other
numbers each occur once. In our employee example, the mode is $100
because that number occurs ten times, which is more than any other
number occurs.
Now, mean, median and mode are all good types of averages, and each
works best in different types of situations. Knowing all three is a
good way to know what kind of data you\'re looking at. But another good
thing to know is the range. For that first company, if the interviewer
had only told you that the salary _range_ was from $100 to $1100, you
might have figured out that you would be making $100. Similarly with
the second company example.
I hope this gives you some good information about why we use all these
different words, and how they can be important to us. Feel free to
write back with any further questions.

 Selected response from: Deb Phillips
 Grading comment Thanks a lot to EVERYBODY, all of you were very helpfull and nice taking out some of your precious weekend time to explain the two terms
Ann 4 KudoZ points were awarded for this answer 
 
Discussion entries: 0 

Automatic update in 00:

6 mins confidence: peer agreement (net): +2 NO DIFFERENCE
Explanation: mean3 something halfway between two extremes. [3 more definition(s)]
Syllables: mean
Parts of speech: noun , adjective
Part of Speech noun
Pronunciation min
Definition 1. something halfway between two extremes.
Synonyms average (1)
Similar Words normal , norm , median , par
Definition 2. the average number or amount, usu. calculated by adding all the values in a distribution and dividing their sum by the number of such values.
Synonyms arithmetic mean , average (2)
Crossref. Syn. average
Definition 3. moderation.
Example the ideal of the golden mean.
Synonyms moderation (1)
Similar Words golden mean , restraint
Related Words mode , middle , compromise
Part of Speech adjective
Definition 1. being between extremes, esp. in the middle; intermediate.
Synonyms intermediate , moderate (3) , medium , median (1) , middle (1,2)
Crossref. Syn. average
Similar Words normal , average , middling , OK , ordinary
Related Words medium , temperate , middle
Syllables: arithmetic mean
Part of Speech noun
Pronunciation ae rihth meh tihk min
Definition 1. the sum of a series of quantities divided by the number of quantities; average.
Crossref. Syn. mean , average
Definition 2. the arithmetic mean gained by adding two or more quantities and then dividing by the total number of quantities.
Example The average of four and six and two is four.
Synonyms mean3 (2) , arithmetic mean
Definition 3. any of several other arithmetic products, such as a median or a batting average.
Synonyms mean3 (2)
Similar Words statistics , figures , totals , median
 Note added at 20020706 10:59:16 (GMT) 
Syllables: average
Parts of speech: noun , adjective , transitive verb , intransitive verb
Phrases: average out , on the average
Part of Speech noun
Pronunciation ae vE rihj
aev rihj
Definition 1. a usual amount or kind; that which is not extreme or extraordinary.
Synonyms standard (2) , norm (1)
Crossref. Syn. normal , mean
Similar Words normal , rule , usual , par
Definition 2. the arithmetic mean gained by adding two or more quantities and then dividing by the total number of quantities.
Example The average of four and six and two is four.
Synonyms mean3 (2) , arithmetic mean
Definition 3. any of several other arithmetic products, such as a median or a batting average.
Synonyms mean3 (2)
Similar Words statistics , figures , totals , median
Related Words ordinary
Phrase on the average
Part of Speech adjective
Definition 1. usual or typical; not extreme.
Synonyms normal (1) , typical (2)
Crossref. Syn. passable , temperate
Similar Words mediocre , common , usual , runofthemill , middling , moderate , standard , indifferent , soso , par , ordinary , gardenvariety , four
Definition 2. obtained by determining the arithmetic mean, in which the sum of the quantities is divided by the total number of quantities.
Example the average daily rainfall.
Synonyms mean3
Related Words mild , mean , simple , routine , medium , adequate , modest
Part of Speech transitive verb
Inflected Forms averaged, averaging, averages
Definition 1. to find the arithmetic mean of (a set of quantities).
Definition 2. to achieve as a typical amount.
Example He averaged six miles a day when running ; He averaged ten dollars a day in tips.
Similar Words total , achieve
Part of Speech intransitive verb
Definition 1. to be or achieve an average.
Phrase average out
 Note added at 20020706 11:40:29 (GMT) 
In statistics, given a list of numbers, the mean is the number which is in the middle whereas the average or arithmetic mean is the number obtained when adding up the values represented by each item on the list and then dividing by the total number of items.
LIST: 1,2,4,5,6
Mean=4
Arithmetic Mean/Average = ((1+2+4+5+6)/5)=18/5=3 3/5
 Note added at 20020706 11:45:57 (GMT) 
If there are an even number of items in the list, the mean is the average of the two middle items. For example, if there are 6 items, let\'s say I lengthen this list by adding the number 7 for a list of an even number of items (6), the mean is 4.5. (The sum of 4 and 5 added together and divided by 2). The average will be calculated by adding the number 7 to the numerator and the denominator in this case is 6 rather than 5. LIST: 1,2,4,5,6,7
Mean = 4.5 = (4+5)/2 (Halfway between the third and fourth items)
Arithmetic Mean/Average = ((1+2+4+5+6+7)/5) = 25/5 = 5
 Note added at 20020706 18:41:55 (GMT) 
arithmetic mean
See mean (cf Mean, Median and Mode Discussion).
average
It is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted means, among other things (cf Mean, Median and Mode Discussion). mean
The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean (cf Mean, Median and Mode Discussion).
median
\"Middle value\" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50% (cf Mean, Median and Mode Discussion).
Mean, Median, and Mode Discussion
Student: When do we use mean and when do we use median?
Mentor: It is up to the researcher to decide. The important thing is to make sure you tell which method you use. Unfortunately, too often people call mean, median and mode by the same name: average.
Student: What is mode?
Mentor: The easiest way to look at modes is on histograms. Let us imagine a histogram with the smallest possible class intervals (see also Increase or Decrease? Discussion).
Student: Then every different piece of data contributes to only one bin in the histogram.
Mentor: Now let us consider the value that repeats most often. It will look like the highest peak on our histogram. This value is called the mode. If there are several modes, data is called multimodal. Can you make an example of trimodal data?
Student: Data with three modes? Sure. Say, if somebody counted numbers of eggs in 20 tree creeper\'s nests, they could get these numbers: 4, 3, 1, 2, 6, 3, 4, 5, 2, 6, 4, 3, 3, 3, 6, 4, 6, 4, 2, 6. I can make a histogram:
Mentor: There are three values that appear most often: 3, 4, and 6, so all these values are modes. Modes are often used for socalled qualitative data, that is, data that describes qualities rather than quantities.
Student: What about median?
Mentor: Median is simply the middle piece of data, after you have sorted data from the smallest to the largest. In your nest example, you sort the numbers first: 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6 eggs. There is an even number of values, so the middle (or median) is between the first and second 4. Because they are the same, we can easily say that the median is four, but if they were different, say if the median was between a 3 and a 4, we would do (3+4)/2=3.5.
Student: So, if there is an even number of values, the median is equal to the sum of the two middle values divided by two.
Mentor: If no birds had nests with only one egg, we would have values of 2, 3, 4, 5, and 6. In this case, the middle number or the median would be the second 4, and we would not need to add or divide because there were an odd number of values.
Student: The last type of averages I would like to know about is mean.
Mentor: Sometimes it is called arithmetic mean, because there are other things in math that are called mean. For example, there is a geometric mean and a harmonic mean. The arithmetic mean of a set of values is a sum of all values, divided by their number. In your nest example,
mean = (4+3+1+2+6+3+4+5+2+6+4+3+3+3+6+4+6+4+2+6)/20 = 3.65
Student: Which one is better: mean, median or mode?
Mentor: It depends on your goals. I can give you some examples to show you why. Consider a company that has nine employees with salaries of 35,000 a year, and their supervisor makes 150,000 a year. If you want to describe the typical salary in the company, which statistics will you use?
Student: I will use mode (35,000), because it tells what salary most people get.
Mentor: What if you are a recruiting officer for the company that wants to make a good impression on a prospective employee?
Student: The mean is (35,000*9 + 150,000)/10 = 46,500 I would probably say: \"The average salary in our company is 46,500\" using mean.
Mentor: In each case, you have to decide for yourself which statistics to use.
Student: It also helps to know which ones other people are using!
I\'m going to wait to talk about range for a moment and concentrate on
mean, median, and mode. Mean, median, and mode are all types of
averages, although the mean is the most common type of average and
usually refers to the _arithmetic mean_ (There are other kinds of means
that are more difficult).
The arithmetic mean is a simple type of average. Suppose you want to
know what your numerical average is in your math class. Let\'s say your
grades so far are 80, 90, 92, and 78 on the four quizzes you have had.
To find your quiz average, add up the four grades:
80 + 90 + 92 + 78 = 340
Then divide that answer by the number of grades that you started with,
four: 340 / 4 = 85. So, your quiz average is 85! Whenever you want to
find a mean, just add up all the numbers and divide by however many
numbers you started with.
But sometimes the arithmetic mean doesn\'t give you all the information
you want, and here is where your first and third questions come in.
Suppose you are an adult looking for a job. You interview with a
company that has ten employees, and the interviewer tells you that the
average salary is $200 per day. Wow, that\'s a lot of money! But that\'s
not what you would be making. For this particular company, you would
make half of that. Each employee makes $100 per day, except for the
owner, who makes $1100 per day. What? How do they get $200 for average
then?!
Well, let\'s take a look:
Nine employees make $100, so adding those up is 9 x 100 = 900. Then
the owner makes $1100, so the total is $1100 + $900 = $2000. Divide by
the total number of employees, ten, and we have $2000/10 = $200.
Because the owner makes so much more than everyone else, her salary
\"pulls\" the average up.
A better question to ask is, \"What is the _median_ salary?\" The median
is the number in the middle, when the numbers are listed in order. For
example, suppose you wanted to find the median of the numbers 6, 4,
67, 23, 6, 98, 8, 16, 37. First, list them in order: 4, 6, 6, 8, 16,
23, 37, 67, 98. Now, which one is in the middle? Well, there are nine
numbers, so the middle one is the fifth, which is 16, so 16 is the
median.
Now, what about when there is an even number of numbers? Look at the
quiz grade example again: 90, 80, 92, 78. First list the numbers in
order: 78, 80, 90, 92. The two middle ones are 80 and 90. So do we have
two medians? No, we find the mean of those two: 80 + 90 = 170, and
170 / 2 = 85. So 85 is the median (and in this case the same as the
mean)!
Now look at those salaries again. To find the median salary, we look at
the salaries in order: 100, 100, 100, 100, 100, 100, 100, 100, 100,
1100. This is an even number of salaries, so we look at the middle
two. They are both 100, so the median is $100. That\'s much better at
telling you how much you\'ll make if you accept the job.
But the median doesn\'t always give you the best information either.
Suppose you interview with a company that has 10 general employees, 7
assistants, 3 managers, and 1 owner. For this company, the mean salary
is $400, and the median is also $400. But you are applying for the
position of general employee, whose starting salary is $100! Why are
the mean and median so far away?
Well, the 10 general employees each make $100. The 7 assistants each
make $400, the 3 managers each make $900, and the owner makes $1900.
If you do the math to find the median or mean, $400 is the answer (try
it!). So what can you do?
The mode is the type of average you want to know in this situation.
The mode is the number the occurs most frequently. In the example for
median, 6 would be the mode because it occurs twice, while the other
numbers each occur once. In our employee example, the mode is $100
because that number occurs ten times, which is more than any other
number occurs.
Now, mean, median and mode are all good types of averages, and each
works best in different types of situations. Knowing all three is a
good way to know what kind of data you\'re looking at. But another good
thing to know is the range. For that first company, if the interviewer
had only told you that the salary _range_ was from $100 to $1100, you
might have figured out that you would be making $100. Similarly with
the second company example.
I hope this gives you some good information about why we use all these
different words, and how they can be important to us. Feel free to
write back with any further questions.
Reference: http://www.wordsmyth.net/
   Grading comment Thanks a lot to EVERYBODY, all of you were very helpfull and nice taking out some of your precious weekend time to explain the two terms
Ann 

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6 mins confidence: peer agreement (net): +1 The are exactly the same....as far as I know.
Explanation: I believe they mean exactly the same thing. Here are some definitions [copied and pasted] from the Random HouseWebster's dictionary:
av·er·age (avÆÃr ij, avÆrij), n., adj., v., aged, ag·ing.
–n.
1. a quantity, rating, or the like that represents or approximates an arithmetic mean: Her golf average is in the 90s. My average in science has gone from B to C this semester.
2. a typical amount, rate, degree, etc.; norm.
3. Statistics. See arithmetic mean.
4. Math. a quantity intermediate to a set of quantities.
5. Com.
a. a charge paid by the master of a ship for such services as pilotage or towage.
b. an expense, partial loss, or damage to a ship or cargo.
c. the incidence of such an expense or loss to the owners or their insurers.
Hope this helps.
Luck!
terry
Above
 Terry Burgess Mexico Local time: 21:54 Native speaker of: English PRO pts in pair: 119

 
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23 mins confidence: peer agreement (net): +1 These are different..
Explanation: mean : statistical term,
average : not statistical,
Average of 14 and 16 is 15, but this is not mean. Statisitical treateatment there required adequate number of sumple. If ssample are, 1, 2, 3 and 4, average is 2.5. This case needlewss to say average is 2.5, too. In the case of average confidential limit cand be use how the mean is confidential. In case of average, there is not the cocept the confidential limit.
  
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2 hrs confidence: Apologies due 
Explanation: My apologies to all who I disagreed with  the average and mean are one in the same. As John pointed out, I was confusing the mean and the median.
I have consulted with my Statistical text books and average and arithmetical mean are the same 
I have hidden my original answer
Again, my most sincere apologies.
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3 hrs confidence: peer agreement (net): +5 Average, arithm. mean, geom. mean, median and mode
Explanation: Average is an inaccurate term, used in everyday language. Often, however, it is used as a synonym for 'arithmetic mean'.
Arithmetic mean: add up all the values, then divide by the number of values (or items).
Geometric mean (fairly rarely used in medicine etc): multiply all the values. Then take the xth root, where x is the number of values (items).
Median: the value, above which (and below which) half of the values (or items, or population) falls.
Mode: the most common (or frequent value). A Gaussian (normal, 'bell') distribution, and many othes, have one mode (singlemode distribution). Many distributions are bimodal, or have any number of modes (think twohumped camel).
E.g.
Take the population 1, 1, 2, 4, 6, 10.
Arithmetic mean (or simply mean): 1+1+2+4+6+10/6 = 24/6 = 4
Geometric mean = 6th root of (1 x 1 x 2 x 4 x 6 x 10) = 2.79
Mode = 1 (there are 2 occurences of the value 1)
Median = 3 (the midpoint between the 2 and the 4)
 Note added at 20020706 17:20:10 (GMT) 
As a medical and scientific translator, by the way, I would never use the term \'average\' in a technical paper. It is simply too imprecise. The correct technical term is mean.
 Note added at 20020706 17:47:39 (GMT) 
The comment made above about dispersion:
The two sets 1, 2, 4, 4, 4, 4, 6, 7
and 1, 2, 3, 4, 4, 5, 6, 7
have the same mean (4), the same median (4) and the same mode (4, yet again).
But the standard deviation of the first is 1.80, and of the second  1.87, because some of the numbers in the latter are further away from the \'centre\'. Because I made sure this happened symmetrically, it hasn\'t affected the mean, the median or the mode.
Therefore, these 3 types of \'average\'  which measure where the \'centre\' is located  cannot tell us anything about dispersion or variance, which is a measure of the set\'s \'average\' distance away from the \'centre\'.
 Note added at 20020708 11:49:41 (GMT) Postgrading 
The selected answer is incorrect. It contains many linguistic, conceptual, logical, mathematical and arithmetical errors. Just for example:
 If there are an even number of items in the list, the mean is the average of the two middle items.
Completely wrong. One counterexample should suffice:
1, 2, 3, 4, 5, 9.
The answerer claims that the mean is 3.5.
It isn\'t; it is 4.
 Mean = 4.5 = (4+5)/2 (Halfway between the third and fourth items)
Arithmetic Mean/Average = ((1+2+4+5+6+7)/5) = 25/5 = 5
It isn\'t; it is 25/6.
 Note added at 20020708 11:51:39 (GMT) Postgrading 
Looking at the above, it seems to me that the answerer hasn\'t grasped the difference between mean and median. What credence should we give to mathemical assertions made by her?
Studied stats at university; used to teach maths
  
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4 hrs confidence: Just to set the record straight.... (points to Terry, I'd say)
Explanation: AAAmedical,
If I understand correctly, your question pertains specifically to Statistics. Within Statistics, "mean" and "average" are exactly the same thing, as you suspect; they are exchangeable. They are not exchangeable however with "median" or "mode", which are other measures of central trend. Also, the fact that "average" in colloquial English has a different meaning is irrelevant for Statistics.
Examples of "mean" and "average" as used exchangeably in Medical Statistics can be found in some of our peerreviewed scientific publications (available in PubMed; search by last name):
• Sgarbossa EB, Pinski SL, Barbagelata A, Underwood DA, Gates KB, Topol EJ, Califf RM, Wagner GS, for the GUSTOI Investigators. Electrocardiographic diagnosis of evolving acute myocardial infarction in the presence of left bundle branch block. N Engl J Med 1996;334:481487.
• Sgarbossa EB, Pinski SL, Gates KB, Wagner GS. Predictors of inhospital bundle branch block reversion after presenting with acute myocardial infarction and bundle branch block. Am J Cardiol 1998;82:373374.
• Sgarbossa EB, Meyer PM, Pinski SL, PavlovicSurjancev B, Barbagelata A, Goodman SG, Lum AS, Underwood DA, Gates GB, Califf RM, Topol EJ, Wagner GS. Negative T waves shortly after ST elevation acute myocardial infarction are a powerful marker for improved survival. Am Heart J 2000;140:385394.
• Sgarbossa EB, Pinski SL, Williams D, PavlovicSurjancev B, Tang J, Trohman RG. Comparison of QT intervals in AfricanAmericans versus Caucasians. Am J Cardiol 2000;86: 880882.
Good luck
Elena
 Note added at 20020706 20:01:43 (GMT) 
Selfcorrection: Below, I meant \"meaning\", with a \"g\" at the end.
  
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13 hrs confidence: peer agreement (net): +1 mean, median (medial), mode (modal)
Explanation: In statistics there is an important difference between these three terms  though the word "average" can be used loosely and confusingly by nonmathematically oriented people to refer to any of them.
Mean = the arithmetic mean (the usual meaning of "average")
Median = the midpoint in a range of values
Mode = The value in a range of values that is most strongly represented numerically, e.g. the highest point in a normal (bellshaped curve)
  
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14 hrs confidence: mean/average
Explanation: All of the answers sofar are good but an average can only be expressed in a liniar sense.
The mean has no confining limits with respect to dimension.
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17 hrs confidence: peer agreement (net): +1 mean=average
Explanation: The question is referring to statistics. these two terms are interchangeable. The average is the sum of the individual values divided by the number of values in the set. The mean, a more "elegant" term as compared to average, is computed exactly the same way.
Mode is the most frequent value in a set on numbers. The median is the midpoint (just as many numbers greater than it as well as lesser than it) in the set of numbers.
Raul Villaronga, MS Industrial Engineering
  
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1 day7 hrs confidence:
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