 Welcome to dealing with materials data, we are going to learn about collection, analysis and interpretation of materials data and we are doing module 2 which is for descriptive statistics using R and so we have been looking at preparing reports and we have looked at rank based and property based reports. So let us concentrate on the property based reports a little bit more. So to do that we have been looking at this data on conductivity. So let us read that file from data. So this is data on copper, ETP copper electrical conductivity, electrolytic tough pitch copper conductivity. So let us first read this information. So it has 20 observations and one variable. So there is this. So it has a header. So we say header is true. So let us say x and it gives you this and we have looked at this data in a little bit of detail in the last session. So what we want to do, so let us just store the conductivity data in this small x. So these are all just numerical values. So x now has just these numbers. Like I said so you can get the mean value of x, you can get the median of x, you can get the variance of x, variance is also called mean square deviation and standard deviation is called root mean square deviation. Now as you can see the measurements of conductivity itself was reported only up to the first decibel place because beyond this the eddy current measurement cannot be accurate so. So when we report the conductivity then we report the mean plus or minus standard deviation. So typically it is reported this plus or minus standard deviation and here it is important not to report the result as 101.32 plus or minus 0.1005249 because beyond this point the rest of the numbers do not make any sense. Of course if you do an algebra you will get but the numbers themselves do not mean anything. So we should take everything up to only the first decimal point or maybe even less than that but at least you cannot report any value in the second decibel place that much is very clear. It should be here or maybe here but it cannot be anything beyond this point. So the right way to report this number now the conductivity of this ETP copper is 101.3 plus or minus 0.1. So this is called the significant digit beyond this digit the numbers have no significance they do not have any meaning and we should not use them. So this is an important point and it is very crucial. So we want to present experimental results and we need to understand significant digits and error when we present the results. So again this is ETP copper and the measurement is in terms of IACS and these are the numbers and what we did is to calculate the mean median standard deviation and variance and standard deviation is called root mean squared deviation RMSD and variance is called mean squared deviation MSD. And because all the conductivity measurements are reported up to first decimal place the mean and standard deviation also should be reported only up to this or less than this it cannot be more than that. So mean is 101.3 standard deviation is 0.1. So the right way to report conductivity for this copper sample is 101.3 plus or minus 0.1 percentage IACS and because we have seen that in the case of this conductivity data the data seems to be a normal distribution. So giving mean and standard deviation is sufficient to completely describe the information. And there is one more point in terms of reporting the error. So we have reported the error as 0.1 so that is in terms of the value itself. So this 0.1 also has the unit of percentage IACS but you can also report it as a percentage itself. You can report 101.3 percentage IACS plus or minus 0.1 percent. There should be no confusion that the 0.1 just becomes 0.1 percent that is not the case and this percentage is with percentage IACS it is with the unit. If you take 0.1 and divide by 101.3 that also happens to be 0.1 percent and that is why it is reported as a relative quantity as 0.1 percent. So it is 101.3 plus or minus 0.1 percent IACS is the correct way of reporting. So the error can be reported in both ways as an absolute error or as a relative error and you can do either way. And one more point that we have to remember is that it is better to be conservative in error estimation. If your calculations give some number like 1.475 for error we should put it up as 2 instead of rounding down to 1.1.475 so it is better to call it as 2 even though you might think that 1.4 or even if it is 1.375 for example which makes it 1.4 we should still report it as 2. This is just being conservative. We are not saying that so if you actually round it off it should be 1.1 say but even then if it is an error if you want to be conservative about error estimates you should always round it up instead of rounding it down so it is a good practice. So this is about significant digits and error we will do more of the analysis on errors later. This is just in terms of reporting the observed values. So we will take a look at slightly more involved data. So we just looked at one property measurement which is conductivity and we found that 20 measurements gave some number and from there we prepared some reports on the rank based and property based values for this data but we can do it for more complicated data also. So we are going to next consider another sort of measurement that is very very common in material science but it is slightly different in terms of how we measure this quantity. So we are going to discuss that in greater detail in the next session. Thank you.