Mean, Median, Mode

In a stack of papers called Instruction.

  • Nov
  • 08
  • 2007

I start out many days of the school year with a Daily, usually a quotation on the board the students have to puzzle over and write about for 5 minutes, but lately they have been questions. In order to add up points on these things (and not add a whole lot of reading on my part), students count up lines they’ve filled in order to figure out how many words they’ve written. We create average word counts and it goes like this:

Date Line Number Word Count
10/2 5  
10/5 4  
10/8 7  
10/18 1  
10/22 3  
10/23 6  
10/26 4  
11/1 9  

We crunch the numbers in order to arrive at a good average of how many words they write on each line. The current goal is 120 words, so each student knows how many lines s/he needs to write to reach that goal. While putting this together the other day, during all periods of English, we ran through mean, median, and mode. “So, we’re getting the mean for all this?” I asked. “Yeah.” “Then what would be the mode?” “4, ’cause you’ve listed that number twice.” “What if I didn’t repeat a number?” “Then there’d be no mode.” Oh…


I know there’s a practical application for mode and median, just as much as there’s a practical application for scanning poetry. Actually, that might be a bad comparison. Still, someone please tell me, because I want to be able to briefly mention it to my students next time, why would I ever need to identify the mode or the median of a set of numbers? The more you place your reason into the world around us, the more likely it’ll sink in and make it out my mouth to my kids.

I’m particularly proud of having even quickly given students a review of mean, median, and mode, but it just made me realize all the times that I’m not doing anything to let kids know that all subject areas are linked.

Do you read papers for grammar, even if you’re not an English teacher? In your P.E. class, would you let a student say “The civil war happened in 1960, when Martin Luther had a dream” without correcting him? Would you non-science teachers let a student slip in “Since the periodic table tells us that the abbreviation for gold is Gd…”? Would you just walk past a student saying “I don’t exercise ’cause it doesn’t matter”? I hope you’re talking to that kid who proudly declares “reading is stupid,” even if you don’t teach reading. Everything is connected and if the ship is sinking, we’re all going to drown.


1. Jackie says:

[11/8/2007 - 7:01 pm]

Yea you! Yesterday one of the seniors dropped off his college essays for editing. My class was shocked – “But you’re a math teacher!”.

Anyway, the mode will often tell us more about a set of data than does the mean.

Example: 78, 78, 78, 42.
Which score better represents the data?

Another example: 42, 78, 80, 82, 83

The median is 80, the mean is 73. The median is more resistant to outliers than is the mean. If these were a student’s scores, would you give them a “C” or a “B”?

Hope that helped.

2. H. says:

[11/9/2007 - 12:06 am]

Here’s an other example of the uses of these measures, posted in response to your entry.

3. Jackie says:

[11/9/2007 - 4:48 am]

Ah – I just read H’s post and was about give you a link. Apparently it isn’t needed.

Keep up the cross-curricular work!

4. Todd says:

[11/9/2007 - 6:09 pm]

I’ll pass that cartoon on and probably put it up on the projector next time we do the average word count. That’s helping make it sink in, H.

Sorry to say, Jackie, but that student would earn a 73%/C in my class. Still, I take your point.

Thank you, both. Those are some ideas to bat around the classroom.

5. H. says:

[11/12/2007 - 2:31 pm]

A longer comment written before the short one above got deleted when I hit “publish,” and here, finally, is the rest:

The mean is useful when you are interested in the total amount of a quantity. For example, if you need to know whether water reserves are at an adequate level, the mean rainfall over the past five years may be more useful to you than the median rainfall. If there were an outlier value of an extremely high rainfall during just one of those years, that would affect your total, which is what you care about in this case, and the median would likely not reflect this information.

In studying the wealth or poverty of countries, the mean income could be useful if you were interested in total resources available, but generally we care more about what income range is typical or widespread, and the median is a better measure of this, as it indicates the fraction of citizens earning more or less than a certain amount rather than the amount of money in circulation. The mode might not be terribly useful because there could be very few citizens having the exact same salary (in the data set 18.1, 18.2, 18.05, 18.02, 105, 105 the mode is 105, but that is hardly a good measure of the central tendency of the data). However, if you cluster data points into income ranges, then, depending on how you choose those ranges, the mode of the income ranges could be informative.

When we did this cartoon in class, a couple students took the roles of the two characters and read the parts. One of my loudest students acted the angry girl, and thought reading a word in upper case a fine occasion for yelling “MODE!” so loudly that I wondered what anyone passing in the hall would be thinking. It was fun.

6. HeavyGod says:

[11/27/2007 - 1:40 am]

Really good and really interesting post. I expect (and other readers maybe :)) new useful posts from you!
Good luck and successes in blogging!

7. Anonymous says:

[1/13/2008 - 9:14 am]

i just read this post when i was searcing uses of mean, median and was really fun to get a question while searcing answer.

8. Clockwork says:

[3/30/2008 - 4:45 am]

How can I simplify why the mean, mode, range and median are used for a year 6 class? (11 year olds)

9. Todd says:

[3/30/2008 - 10:35 am]

Clockwork, did you look at the comic H posted earlier? Looking at H’s previous explanation might help, too.

10. Nicola says:

[12/22/2008 - 9:02 am]

I am a manager at a movie theatre which hires mostly high school students (first job). I am currently completing my education degree. On a typical weekend I help about 10 students improve their writing by going over their essay with them. I hope it helps, because it’s killing my payrole : o) But they are just so eager to succeed and know that they need help. Getting it from an employer give them a huge morale boost, it shows someone else outside of school cares about the education that they receive.

We kicked this idea of who’s job is it to correct grammer around in a mandated Teaching LIteracy class at UC. The mat people were totaly against it. We suggested giving list of common errors they find in student’s writing to the english teacher if its block , or simply talking to the english department. Shouldn’t take off points or get bogged down in it, but should def. try to help students become better communicators through the written word.

11. DILSHANA says:

[4/9/2011 - 5:57 am]