# How to estimate your score for an HSK practice exam?

I'm preparing for my first HSK exam in October - probably level 1 - so I completed a practice exam. I know the number of correct answers, but I don't how to convert these into a score.

From what I've read, it's not a simple matter of dividing the number of correct answers by the total number of questions and then multiplying by the maximum score. Apparently the score is calculated by comparing with other students.

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I had 11/20 correct answers in the listening part and 19/20 in the reading part. So at least I know what to work on :-) – Sjors Provoost Sep 13 '13 at 20:03
As high as you could. – congliu Sep 15 '13 at 5:45

To pass any level of the new HSK, you have to beat 74.75% of the total.

That is to say, for this case

if 74.75% of the total had done worse than that (i.e. as the weights of listening and reading are 1:1, such many people had correctly answered less than 30 questions), you will pass the exam.

For "Is there at least some sort of heuristic, like: if you answer X percent correctly, you'll probably pass?", the answer is maybe. There may be some historical data that you can refer to. They serve as important references, but you cannot 100% trust them, if the HSK exam you take is specially more difficult or easier than former ones.

### Why 74.75%?

From the official website of the HSK, we know

``````+------------------+--------------------+---------+
| HSK Score(Total) | HSK Score(Section) | Percent |
+------------------+--------------------+---------+
|              400 |                100 |      99 |
|              277 |                 69 |      90 |
|              250 |                 63 |      80 |
|              231 |                 58 |      70 |
|              215 |                 54 |      60 |
|              200 |                 50 |      50 |
|              185 |                 46 |      40 |
|              169 |                 42 |      30 |
|              150 |                 37 |      20 |
|              123 |                 31 |      10 |
+------------------+--------------------+---------+
``````

And from its description:

A section score of HSK (Elementary-Intermediate) is a scale score with 50 as the score mean and 15 as the standard deviation, while the total score is a scale score with 200 as the score mean and 60 the standard deviation ... The right column indicates the percentage occupied by those whose scores are lower than the corresponding scores in the standard HSK reference group.

It is easy to verify via the table that a section score meets the normal distribution (with with 50 as the score mean and 15 as the standard deviation), so is the total score (with 200 as the score mean and 60 the standard deviation).

HSK=50+15×Z

Where Z can be considered as a Gaussian variate with 0 as the mean and 1 as the standard deviation, and then the HSK for a section is a N(50, 15^2) Gaussian variate. By observation, we can find that, there're some regular patterns for the setting of the total score. If an exam has 4 section, the setting for total score is a N(200, 60^2) variate. Consider these passing scores

HSK level 1-2: listening (100), reading (100). Total (200). Passing: total score >= 120.

HSK level 3-6: listening (100), reading (100), writing (100). Total (300). Passing: total score >= 180.

We can conclude that at level 1-2, the total score is a N(100,30^2) variate, and at level 3-6, N(150, 45^2). Thus we can see that in the standard Gaussian cumulative distribution function:

Φ[ (120-100)/30 ] = 0.7475

Φ[ (180-150)/45 ] = 0.7475

PS: it seems in the old HSK, the weights of listening, grammar, reading, and comprehensive sections are with this ratio `1:0.6:1:0.8`. However if we try the weighting formula for the old HSK total score

HSK = [ (Z1+0.6×Z2+Z3+0.8×Z4) / 3.4 ] ×60 +200

where `Z1,Z2,Z3,Z4 i.i.d. ~ N(50,15^2)`, the final HSK will be a N(200, 30.566^2) variate, which is a contradiction to another definition N(200, 60^2). Anyway, as the math model hasn't been rigorously stated, my answer considers N(200, 60^2) as the correct one because its CDF value examples are well listed.

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Thanks for the explanation of how the scoring works. So this means that only 25% can pass each exam, by design? Now I just need a way to figure out how many correct answers that 25% typically gets. – Sjors Provoost Sep 16 '13 at 8:13
@SjorsProvoost Yes, its passing rate is controlled to be around 25%. I understand the expectation number of correct answers that 25% gets is what you need, but sorry I can't find such information on the Internet. In user3232's answer, maybe the "Gurulu" he suggested can help you. Anyway I believe his 60% is a good guess, because most exams in China set their passing score to 60%, so might the difficulty of HSK follow that. – Stan Sep 16 '13 at 8:34
they can't both be true. I'll look at Gurulu, but I'll leave the question open for now. – Sjors Provoost Sep 16 '13 at 8:57
@SjorsProvoost By carefully controlling the difficulty, the error can be limited in a bound. I've just found this wonderful article talking about the algorithm and it offers information about the reference score in 1988 and 1991! Scaling your 11/20 listening and 19/20 reading score into those two years, your final score would be 155 in 1988 and 156 in 1991. (Congrats you will very probably pass.) We can see that the difficulty is designed quite well. – Stan Sep 16 '13 at 9:39
Yet, it's better to know recent `raw score -> HSK score` tables, especially those after 2010. Hope others can help you find that :D – Stan Sep 16 '13 at 9:54

Gurulu estimates your likely HSK score based on any number of HSK practice questions you have answered preparing for your HSK.

To pass the new (new since 2010, https://en.wikipedia.org/wiki/Hanyu_Shuiping_Kaoshi) HSK Test with levels ranging from the beginner HSK 1 to the advanced HSK 6, you generally have to answer approximately 60% of the questions correctly, give or take a little, depending on minor adjustment made by Hanban taking into account the performance of all students taking the test at a specific level at that specific time.

The old HSK was scored by averaging the results of all students. A score of say 50 simply meant that one was just about average.

The new HSK is not scored like the old one, the score of the new HSK test is proportional to the number of questions answered correctly. It is likely that minor adjustments are still made to scores based on everyone's performance that day.

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Where does the "60%" come from? As "the score is calculated by comparing with other students" is true (you can verify this in the official website), this "60%" data is either not true, or, experiential (then that is what OP needs :D). – Stan Sep 16 '13 at 2:35