50% of Students are Below Average
People place a lot of importance on being “above average” — but should they? Your position in relation to the average can be interpreted in many complex ways. Let’s unpack it. We’ll focus on test scores in this article since that is the most relevant application for our students, but these ideas are useful in many contexts.
What is an average? — It’s a measure
In order to establish a statistical average you must first have quantitive data, that is, that you must compress each student’s months of hard work, depth of understanding, and broad problem-solving abilities… into one single number. Before you go putting any amount of your self-esteem into a score, ask yourself this: do you really think that your intelligence, skills and adaptability can be summed up in one number? I don’t think so.
Let us imagine that a test score is more like looking at one frame of a video.
Sure, this is an accurate image of Gaston. He really did look like this for a moment.
But does this one image give us a good idea of who he is as a whole?
If you’ve ever paused a video of yourself, you know that the image of you with one eye open and mouth agape is an image of you, but does not accurately represent what you actually look like. Your test scores are the same.
Tests are like group photos:
In any one image there will always someone pulling a weird face or blinking. Tests can also give us bad scores just because of bad timing.
Now consider what to do with all the “snapshots” of the test takers. Everyone has one number that represents them and it might just so happen to capture a particularly flattering or unflattering moment for that person. How might we process this data?
Rank and the Median Score
One of the easiest things you can do with test scores is rank them. The highest score gets rank 1, second highest gets rank 2 and so on.
There are benefits to ranking scores:
You get a winner! Do you want to glorify getting top marks? This is the way to do it. (but should we glorify top marks? Read this article)
If you know how many scores there are then you know where you sit in relation to the median (a kind of average).
The ATAR — Australian Tertiary Admission Rank — is a rank. It does not matter how much better one student scored from another, it only matters that they scored better. The top ~50 students get 99.95, the next group get 99.90, and so on. For HSC students in particular, rank is simply a more relevant measure to estimate eventual ATAR performance.
However, there are also detriments to ranking students:
Students cannot infer how far behind they are in terms of actual exam performance. The 5th ranking score could be 20% lower than the top score, or it could be 1% lower.
Ranking at the bottom of the class is devastating. A single low score can be damaging enough to a student’s self-esteem that they may never recover from the perception that they “are bad at” that subject or school in general. If the scores are public, this can extend to a harmful perception from other students as well.
If you’re not at the top or the bottom of the class — as is the case for almost all students — the rank you probably care about the most is the median. In a class of 25 students the median mark is the 13th highest mark (median = middle).
Consider the class below. There are 26 students each represented by a dot. The median score is the score halfway between the 13th and 14th scores, both of which are 6 so the median is 6.
Graph made with Geogebra
Imagine that you don’t know what the whole distribution looks like and you are told that you are rank 20th. You might think “oh no, I’m 7th lowest in the class, that’s so bad,” but look! the 7th lowest score is 6! You would be doing just as well as the 10th best student! Similarly, the student ranked 9th in this example should be feeling just as happy as the student ranked 2nd!
Crucially — half of the students will be told that they are “below average.” “Average” may refer to median or mean which are both equal to 6 in this example. 13 out of 26 students may perceive this exam as a failure even though 7 of those did no worse than the median score.
In a real-life scenario it’s unlikely that so many students would have exactly the same exam mark as they do in this example, but here the 11 students who scored 6 may represent 11 students who scored between 60 and 70 percent on the exam — not enough of a difference to put any stock into.
Do You Need to be Above Average?
It all depends on who you’re comparing yourself to. Remember, the average score is the average score of your peers. If you expect that everyone in your class is going to get a result you’d be happy with, you do not need to be above average — indeed, you could be dead last and still be happy. There is no point in comparing yourself to the average just for the sake of status or competition. Ask yourself what that number represents.
If you're approaching Year 11 and 12, it's worth trying to find the average ATAR of your school (if you have an ATAR you're aiming for). Students are often shocked to discover that the average at their school might be an 80, or even a 90 ATAR. If you need an 80 to enter, say, a Bachelor of Science at USYD and the average ATAR of your school is 90, you can be considerably below average and still get the score you need! Unfortunately, the variation between schools is huge, and at less privileged schools the average can be much lower (the national average ATAR is 70 by design).
Schools encourage students to push themselves to get as high an ATAR as possible for both good and bad reasons. A high ATAR allows students to access many university courses and potentially receive scholarships. However, a high average ATAR amongst its students is financially valuable to a school. Advertising a high average allows schools to attract students and increase tuition fees. If you’re aiming high, make sure you’re doing it for your own benefit first and foremost.
These are the University of Sydney’s admission statistics for 2024.
The lowest ATAR to receive an offer, 60.8, is well below the national average of 70 — even Australia’s most competitive university accepts “below average” students.
Finally, many parents cling onto the notion of their child being “above average” as a proxy for their child being “safe” or their parenting being “good enough.” There can be much comfort in the label for parents, for whom the schooling world is obscure and anxiety-inducing. However, we tutors see too many parents panic when their child is no longer scoring consistently above average. Don’t worry. Half of all students are in that category — they’ll be okay. Below average is a very normal place to be.
The most important thing is for below average students to not be detrimentally affected by faltering confidence or self-esteem. Below average students are just as worthy of the labels “smart,” “hard-working,” and “good learner” as any other student.
Do you need help recovering from a “bad” score? Tutoring can help you regain your confidence — not only my improving your grades, but by helping you to appreciate the extent of your talents not quantified by test scores. Future Tutor has places available for all students, regardless of how you compare to the average.