What is the measure of consistency in the data?

Please find below the marks of the students in ten tests.

How do we rank them to reflect consistency through statistical tools?

Student 1|100|100|100|100|100|100|95|98|98|99|
Student 2|100|100|100|100|100|100|100|95|97|98|
Student 3|100|100|100|100|100|100|100|100|95|95|
Student 4|100|100|100|100|100|100|100|100|100|90|

All 4 students have the same average. But in my opinion, Student 4 is more consistent, then Student 3 and finally Student 1. How to support this through statistical tool?


Hi @Ashwin,
Thanks for asking this in such an interesting way.
There are various methods of measuring consistency, but one of the famous methods is to find coefficient of variance.
You can compute it as : (standard deviation/ mean) *100

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What is the measure of consistency then? Higher value means more consistent or lower value means more consistent?

If I calculate coefficient of variance, then the values are
Student 1 - 1.649488
Student 2 - 1.7816507
Student 3 - 2.1294799
Student 4 - 3.1942199

A higher value of coeff. of variance depicts inconsistency of the student. The lower the value, more consistency will be there.

But if you look at the data, Student 4 with higher value is more consistent as he has scored nine 100s out of 10, whereas Student 1 with lesser value has score only 6 100s out of 10. So student 4 is more consistent. Isn’t it?

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Can someone help me with this?

I’m not sure about the whole proof of this, for more info, you can refer this

Just in order to help you out, you can take an example where the data can be compared quite easily.
Ex: Introduce a student 5, which is way more inconsistent. and compare the CV score.

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