when the students ask the teacher can you curve what exactly do they mean a can you
graph y=e^(-x^2)? b can you play baseball or c can you give us extra credits so i'm from Taiwan
but i haven't been back for so many years anyway apparently in taiwan a lot of teachers will help
the students by taking the square root of the exam scores and then multiplied by 10. and when i first
heard of that it got me really interested because i could figure out how mathematically it will help
the students but i just don't know why they choose to do it like that so in this video i will to
demonstrate four different methods into using the one i just mentioned and you guys can let me know
which one you think is the most fair which one you think is the most beneficial for the students
i don't do any of that for my classes don't hate me on my students but anyway before we
continue i would just like to address that a lot of students have asked me
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datacam for sponsoring this video ok here we go as we can see i gave you guys 10 students exam scores
and yes i just made those up i know it's not that realistic because i didn't include any zeros but
it's okay anyway if we use the usual grading scale then we will see we will only have one a
one b one c two d's and five f's and by the way b's and f's they are not passing
so let's see what we can do to help the students the first way the first curve is the taiwanese
teacher's way which again we are going to take the square root and then multiply the result by 10. so
what exactly do we get imagine if a student gets 100 points originally take the square root of that
which is 10 and multiply by 10 well the student is still going to get 100 points i think this
is one of the reasons why that the teachers love this because nobody can get above 100 points okay
i don't know and next number though let's take a look at d1 because this will give us 90 and then
so with this curve we see that if we get 49 points then we can actually pass the class so that's
pretty nice and now let's see how many people are going to get a well we are looking at 81
or above so in fact this person will actually get an a onto this curve right so we have two a's now
that's cool that's really nice huh and how many b's are we going to get from 64 to 81 right less
than 81 of course so we're talking about this person only so we just have one b okay and then
how many c's are we going to get so 49 and less than that right so we are talking about
this this this and that so four c's oh my goodness and then how many d's 36 to 49 so
this person only so one d and then we still have two people failing so two f's
so take a look and compare with the original of course this is much better
but i don't know and before we do the next one let me just tell you guys about
why this works so when we take a square root of a number let's say the original is just x
and then multiplied by 10 we can write that as the following that's just 10 times square root
of x and in fact this right here is bigger than or equal to x if x is in between of 0 and 100
and that's why this right here can help the students but now you might be wondering how
in the world did they come with this formula right well i'm not exactly sure but this is just going
to be my guess so the idea is that we have to utilize the fact that when we have the square
root of x this right here is actually above just x well from where to where though from zero to one
and you see the trouble is that our exam scores they are all from zero to one hundred so this is
what we have to do starting with our original score we will have to divide it by 100 first
so we're looking at x over 100 and now the x value is between of zero and one and then we take the
square root so take the square root and on the top we'll just have square root of x and on the bottom
we will have 10. okay but now you see earlier we divided by 100 so we should multiply by 100 right
so when we do that of course they cancel and we end up with 10 square root of x so that's my guess
but whoever came up with this in the first place i think that's pretty genius
now let's face it when students ask you can you curve you know they just want extra credit so
for the second way why don't we just look at everybody's score and then just give everybody
a bonus 15 points so let's have a look originally if you have 100 points and now you are going to
get a total of 115 okay so you do get the detour bonus even though you had the a originally already
but it's okay it will feel much better right and then if you have 85 guess what wow it looks
like you have a perfect score 100 now and then if you have 75 this is going to give you the a
this is going to be super fair in this sense everybody has that 15 points extra credit and
now let's just take a look real quick how many a's b's that we are going to have well for ace
we're looking at 75 or above so oh actually we have this this and that we have three a's now
wow look at that and let's see how many b's 65 to 75 no b's and then c let's see 55 to 65 so we're
talking about this this this and that so four c's and d we have no these right now these and lastly
we have this this and that they are still going to get the f okay so wow look at that this is
this is pretty like a normal right cool and of course this works perfectly because everybody gets
15 extra credit so the idea is that originally if you take a look at this is just y it's equal to x
yeah everybody plus 15. so this is not really like a curve it's actually just a vertical shiftment
and you are going to have this so this is going to be y equals x plus 15. and now this is the
normal way to do this yes we'll be utilizing the normal curve so for the third way let me write
that down right here for you guys and in order to do this we need two important statistical values
the first one is the mean which is just the average we add everything and divide it by taking
our case and the notation for that is mu and i have computed for you guys already this is 59.3
and the other thing that we need is called the standard deviation denoted by this sigma here
and the best way to compute this is you enter everything onto a spreadsheet and use
the building function to compute the standard deviation and you will get approximately 21.7
and if you guys want to see how to compute this standard deviation by hand
just leave a comment down below and let me know but anyway how can we utilize this and that
to help us assign grades for the students well let's go ahead and draw the normal curve which
is just like a bell-shaped curve so i'm going to put it down like this for you guys like so
and as we can see this is symmetrical right in the middle this is where the ming is which is
59.3 and we are going to just go from the min and then we are going to add one standard definition
so you do this plus that and let's say we will get to here and if you add them up we will get 81
and then let's just go ahead and do it again so this plus that we will get 102.7
and of course start from the mean and then subtract one standard deviation we are going
to get 37.6 and then do it one more time we will get 15.9 cool now this is the breakdown we are
going to make some cuts here here not right in the middle and then here and here you guys ready
this little region is the amount of ace and then here it will be the b and you see the majorities
will be getting c's and then this right here is where the these are and then lastly is the
f so based on this let's see how many a's are we going to get did anybody get above 102.7
no nobody so no ace no ace i don't know what you guys feel but yeah anyway how many beats are we
going to get so we're talking about from 81 to 102.7 and let's just be nice let's include an 81
in our case all right because it's right there so i'm just going to include it just to be nice
so i'm going to say two okay and then for c well we're talking about from here to here
not including 81 so we're looking at 37 so we are talking about one two three four five six okay we
have six c's and how many d's are we going to get from 15.9 to this okay these two people now
they don't have f's anymore they have these and okay nobody got below 15.9 so
we are not giving out any f's this right here is i don't know how to just feel but
yeah that's the normal way to do it okay for the last way i think this is the most realistic
way because in real life everything is competitive if you're talking about applying
for jobs they will rank you right from the best applicant to like the least applicant
and things like that so in this case because we have five letter grades to be assigned it
let's just go ahead and make it even we are going to have 20 of each letter
grade so of course we will have to arrange the scores from the smallest to the biggest
and because we have ten scores divided by five well that means two people are going to get a's
and then two peoples are going to get b's and then two more people are going to get c's and then
lastly we see that okay these people are going to get these and of course we have the f's right so
i think this is the most fair way but in this case the scale is going to look something like this
so we are talking about let's say 81 or above and then we're talking about 63 or above
and then we're talking about 58 or above and then 40 were above and of course below 40. yeah so
this right here will be the a's and then b's c d's and s so this right here if you do implement this
curve you can always have like the same number for all this right here so a b c d and f
guess what this is just going to be 2 two two two two so i think this right here
could have been the most fair way in my opinion i would prefer to do either this which i know a
lot of students wouldn't like it or i would just do the second way which i will just add 15 points
to everybody's score so let me know what you guys think and be sure you guys check
out datacam if you want to learn more about datasets and as always that's it