mean/average
English translation: Mean: precise statistical quantity. Average: fuzzy everyday expression.
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| 10:50 Jul 6, 2002 |
| English language (monolingual) [PRO] Science / statistical data | |||||||
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|  Selected response from: Deb Phillips (X) | ||||||
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| SUMMARY OF ALL EXPLANATIONS PROVIDED | ||||
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| 5 +5 | Average, arithm. mean, geom. mean, median and mode |
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| 4 +2 | NO DIFFERENCE |
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| 5 +1 | These are different.. |
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| 5 +1 | mean=average |
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| 4 +1 | The are exactly the same....as far as I know. |
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| 5 | Apologies due - |
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| 5 | Just to set the record straight.... (points to Terry, I'd say) |
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| 4 +1 | mean, median (medial), mode (modal) |
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| 5 | mean/average |
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| 4 | There is a difference. |
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| 4 | definition |
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| 4 -1 | in English there are 3 kinds of averages: mean, mode and median |
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Answers
6 mins confidence: 
peer agreement (net): +2
peer agreement (net): +2NO 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 2002-07-06 10:59:16 (GMT) -------------------------------------------------- Syllables: av-er-age 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 , run-of-the-mill , middling , moderate , standard , indifferent , so-so , par , ordinary , garden-variety , 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 2002-07-06 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 2002-07-06 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 2002-07-06 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 so-called 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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