previously we looked at a nice list of all the instruments that you could be using in a levels to measure different kinds of quantities now we want to look at what if you took one of these instruments and you measured something some quantity you are not very certain of that quantity but how do you find or estimate the uncertainty that's what we're going to look at in this part so let's say you are trying to measure the diameter of a round thing a glass marble or like some kind of you know round thing here your like huh how do I measure diameter take a few diameter I measure or maybe it is something really soft like this squishy soft I don't know what you call this thing pillow see this squishy soft thing it goes you have a diameter but it can be you know squash and you try to try your best to measure it will not be the same value so as you can see on this set of data here you have slightly different diameters of a glass marble somehow this glass marble is not perfect how do you estimate uncertainty the number one method if you have many readings of the same thing such as a marble you say oh I take diameter here I think that's the middle I do another time I measure here I do another time I measure here I do another time I measure here it's it's hard to know exactly what diameter is so if you have five values here we are going to take half the range of the method so the uncertainty in D I use a triangle the Delta to show uncertainty will be half the range what does half the range mean half the range basically says oh this take half I'll just write it here half the largest value minus the smallest value also known as D Min what would that be in our case here if you look at the top list I think smallest is this one 2.48 the largest is is this one 2.52 so this will be our D Max minus it you'll get 2.52 - 2.48 and these are all in cm and that would give us after calculation a value of 0.02 this is CM CM okay that is our uncertainty Delta D note this is the absolute uncertainty how do I know absolute cuz you know my Val are in cm so also in cm but we're not done yet usually you will want to write it uh with the answer the the actual value of D so maybe I can find the average diameter how do you find average you add up all together 2.52 + 2.49 + 2.48 + 2.51 + 2.49 oops that's four divided by the number of measure M there are so that's 1 2 3 4 5 so I write five and our average will be 24984 uh my calculator says 498 okay 2. 498 CM so that's great now I have my average and I have my CM so I conclude after all my measurement that the the measurement of D conclusion therefore it will be uh 2.50 but I'm not exactly sure cuz my measurements a bit different so I say plusus 0.02 I am uncertain and since both of these quantities are in cm so I can put this plus minus y value and the CM is on this side so you can kind of say okay like this whole thing is under a bracket all right that's how we know I'm kind of sure 2.5 but some variation so this is one method you will use a lot in paper three let me write it U up here where am I #t paper three but a lot more also in paper five where you take measurements and you find the uncertainty there is one more method though there is one dangerous thing whatever um half the range method okay so this one the main equation you need to know or write down for your notes is half the range that's how you find how that's how you estimate uncertainty but there's a danger if you get zero uncertainty you cannot use this method so uncertainty this is a note warning sign un certainty whatever you use if this method cannot be can I move over this side Bit Zero so the whatever uncertainty you find with half the range cannot be zero if it is zero you cannot use this method then how so in paper tree there's another method this other method is to just estimate all if you cannot have the range do some estimation so you kind of have this round shape which is kind of round but not really and you say I can measure the diameter I don't know it's maybe 2.5 based on what I think I measured but I'm kind of Uncertain if I use my ruler like we mentioned the other day the smallest reading of a ruler is 0.1 CM so maybe I'm like hm maybe I'll take two times or five times I I just estimate just choose a value so I'll say okay maybe I'm I'm not sure 0 0.3 this is a squishy toy maybe I'll put 0.3 so this value just came not out of the blue but I estimate it and this is also a skill you will need to know in paper three only no paper five over time the more experiments you do uh you will get more used to estimating there's no really fixed equation for that but estimate look through some part past years and see what are the allowed ranges of estimated uncertainty and that's how we build experience okay so do your live experiments make sure you know the two methods have the range and just estimate gu estimate your way through next up we're going to look at how do you interpret your uncertainty so you know oh I have a 0.3 uncertainty here for example what does that mean for my data how valid or how accurate is it