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My textbook sets this question:

In each of the following sentences, a word has been used in sentences in different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

The average of 3, 4, 5, 7. and 10 is 6 whereas the mean is 5.

The books says that it is wrong and median should be used instead:

In this sentence, mean has to be replaced with median for the sentence to make sense.

My question is: isn't mean correct? For years I've studying the word mean in mathematics, and now the book says: use median.

I don't think the sentence is wrong due to the mean being written as "6", because even if I write the wrong mean, the usage of the word is correct, I'm just writing the wrong answer.

More Sources

If you look at this link, it says, mean should be used for symmetrical data sets, and median for skewed data, In the above sentence, the data being skewed my guess is that is probably the reason median is being used and not that mean is written as 6 whereas actually median is 6.
Mean or Median

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closed as off topic by Jasper Loy, Mehper C. Palavuzlar, kiamlaluno, Mitch, Daniel Jul 20 '12 at 17:52

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Sorry, I had to commute. @KartikAnand the passage you quote is saying that 5, not 6 is the median. It says that 6 is the average, which I take to be mean (rounding up). –  Matt Эллен Jun 28 '12 at 16:53
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To my mind, the biggest problem with the textbook sentence is its use of the ambiguous word average while trying to emphasise the correctness of median over mean. –  Brian Nixon Jun 28 '12 at 19:24
    
Also the Median cannot be 6, six is not present in the sample. As explained by your source "The median is the middle value in a sample sorted into ascending order". –  Matt Эллен Jun 28 '12 at 20:54

2 Answers 2

up vote 4 down vote accepted

It is wrong to say "the mean of this set of numbers is 5". Not grammatically wrong, but mathematically wrong. The sentence could be made correct by changing it to, "the mean is 5.8", or you could change it to, "the median is 5". If the writer's intent was to tell you the median, then the error is saying "mean" when he means "median". If the writer's intent was to tell you the mean, then the error is saying "5" when the correct value is "5.8". As the sentence also mentions an "average", which is normally understood to be the same as "mean", it seems likely the intent was for the last number to be the median.

You seem to be getting stuck on the idea that the sentence could be corrected other than by changing "mean" to "median". Well, sure. Any time someone says, "How would you correct this sentence?", there are likely thousands of possible changes. Suppose someone said, "Thomas Jefferson was the first president of the United States". I could correct that by replacing "Thomas Jefferson" with "George Washington". I could replace "first" with "second". I could insert "Democratic-Republican" between "first" and "president". I could replace "Thomas Jefferson" with "Yuri Gagarin" and "president of the United States" with "human to travel in space". Etc etc.

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But why would an English book consider something mathematically wrong as wrong, its like a semantic error in programming, it doesn't do what it is supposed to do but "syntactically" according to the language it is correct. In the same way, writing 6 is semantically or mathematically wrong, but where English usage is concerned, it is correct or is it according to what the link says? –  Kartik Anand Jun 28 '12 at 16:00
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The sentence as given is not grammatically wrong, but it is still wrong. The writer of the sentence has either made a math error or he doesn't understand the definitions of the words he's using. All I know about the book you're referring to is your quote above, but it appears that the book is trying to say that the writer is using the word "mean" when he should use the word "median". As I said above, there are many ways you could change the sentence to make it correct. You're getting hung up on this idea that you could fix the sentence by changing the number. But that's not ... –  Jay Jun 28 '12 at 16:13
    
... the author's point. He's trying to explain the difference between "mean" and "median". Sure, you could make the sentence true by changing it to, "The mean is 5.8". You could make it true by changing it to, "The Mean is the name of a bar in my home town." But that's irrelevant to the point the writer is trying to make and does nothing to help anyone understand what the writer is trying to say. He's trying to explain the difference between mean and median. Just accept that instead of arguing with the poor guy about why you want to talk about some other question. –  Jay Jun 28 '12 at 16:21
    
@Jay sorry but I was not arguing actually I was too hung up on the fact that there should be a grammatical error not a mathematical one, but I guess that's the case :) –  Kartik Anand Jun 28 '12 at 16:25
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@Kartik; One final attempt. Change the 7 to an 8 (assuming a misprint). Then the original sentence still contains an error, because the mean is 6 and the median 5. The author makes the point that mean is the wrong word, and should be replaced by median. To a non-mathematician, that's as much a grammatical point as is the difference between disinterested and uninterested. –  TimLymington Jun 28 '12 at 22:57

Median is the middle value of a list of order numbers. In 10, 45, 600, 601, 615, 777, 999 the median is 601. The mean is the sum of the numbers divided buy the count of the numbers, for the above example that is 521.

Mean, median and mode (most popular number) are all types of average.

This is how it was taught to me, albeit long ago and with many more examples.

Your book asks if mean is the correct word when presenting the median number of your list. It then tells you that mean is wrong and median is correct, so that is fine.

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My question is not the meaning of mean or median, but why is using mean in the above sentence wrong. Its an English language question, not a mathematics one where the answer should matter –  Kartik Anand Jun 28 '12 at 15:16
    
Right, so it should be median, because the mean is not 5, it is 5.8 –  Matt Эллен Jun 28 '12 at 15:17
    
Thats what I'm saying the reason given for not using mean is not that the value "6" is wrong rather, that median is more apt here –  Kartik Anand Jun 28 '12 at 15:18
    
It's a misprint. Rather an unfortunate misprint, but this sort of thing does fall through proof-reading. –  Andrew Leach Jun 28 '12 at 15:20
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I may well have misunderstood "The question was..." Which question are we talking about? Context, context, context! –  Andrew Leach Jun 28 '12 at 15:23

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