GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)  


10:50 Jul 6, 2002 
English to English translations [PRO] Science / statistical data  


 
 Selected response from: Deb Phillips (X)  
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Summary of answers provided  

5 +5  Average, arithm. mean, geom. mean, median and mode 
 
5 +1  These are different.. 
 
5 +1  mean=average 
 
4 +2  NO DIFFERENCE 
 
5  mean/average 
 
5  Just to set the record straight.... (points to Terry, I'd say) 
 
4 +1  mean, median (medial), mode (modal) 
 
5  Apologies due  
 
4 +1  The are exactly the same....as far as I know. 
 
4  There is a difference. 
 
4  definition 
 
4 1  in English there are 3 kinds of averages: mean, mode and median 

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/ 
 
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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 
 
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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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in English there are 3 kinds of averages: mean, mode and median Explanation: The mean is what we normally call the average.  Note added at 20020706 11:28:54 (GMT)  To use its proper name, the arithmetic mean: \"The value obtained by dividing the sum of a set of quantities by the number of quantities in the set. Also called average.\" The American Heritage Dictionary of the English Language The median constitutes the middle value in a distibution, whilst the mode is the value that occurs most frequently. If your text is statistical in nature, you should use \"mean\", whilst in everyday language \"average\" is fine and has the same meaning.  Note added at 20020706 12:47:32 (GMT)  \"Mean: Mathematics. a. A number that typifies a set of numbers, such as a geometric mean or an arithmetic mean. b. The average value of a set of numbers.\" The American Heritage Dictionary of the English Language  Note added at 20020706 12:49:48 (GMT)  Just in case you\'re wondering what the geometric mean is, here\'s a definition: \"Geometric mean: The nth root, usually the positive nth root, of a product of n factors.\" The American Heritage Dictionary of the English Language 
 
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There is a difference. Explanation: "Average" is a word of daytoday language and is rather loose in its meaning. It can be applied to all types of average. "Mean" is one of the specific types of average which are formally defined in statistics. It is the sum of a list of numbers, divided by the total number of numbers in the list. (The other main types are "median" and "mode".) See my reference for a clear and simple explanation of statistical averages. Reference: http://www.shodor.org/interactivate/lessons/sm1.html 
 
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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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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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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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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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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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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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definition Explanation: mean is more precise, while average is a "ballpark" figure. You talk about Mean Greenwich Time, but average attendance at football games during a season 
 
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