# Representing uncertanties

Lots of us are at the place where we have all of our data and need to start drawing graphs and working things out. Depending on the equation you are working with you will draw a different graph (it is unlikely you will just be plotting the variables you measured). For example those of us dropping balls to determine g will be plotting s vs t^2 (s=1/2gt^2).

First of all decide on the uncertanty on each measurement. You might use the resolution of the instruments. You might need to take account of response time. You might be able to measure the uncertanty (talk to Becca and Tom about what they are measuring with their lasars). We alway use the largest uncertanty not an average of them.

You will then to process your uncertanties (depending on your formula). Let’s say we have measured a time of 5.0 s with an uncertanty of +/- 0.2 s. That means our maximum time will be 5.2s and minimum 4.8s. For our dropping balls experiment we want t^2 so we square each of these giving t^2 = 25.0 s, t^2 max = 27.0 s and t^2 min = 23.0 s. This then gives you your point to plot on the graph with error bars (n.b. when you process the data like this you may well end up with uneven bars – this is fine).

When combining data (working out stress say) you have to be a bit clever.

stress = force / area.

stress max = force max/ area min.

stress min = force min / area max.

You can have a play with the numbers and see what gets you thte biggest and smallest values. Doing all this on excel (other spread sheets are avaliable) will make your life so much easier than trying to do it all by hand.

You can now plot a graph with error bars (we should really call them uncertanty bars). Draw your line of best fit (which should be straight as you have thought about what to plot) – it must go though all the uncertanty bars. Work out the gradient and calculate the quantity you are measuring. You should then draw the steapest and shallowest lines which still go through all the uncertatnty bars. The gradients on these will allow you to work out the uncertanty on your quantity. Do what you can and we will look at it next week.