hello again and welcome back to operations management we're continuing our series on the seven tools of quality and this time we're going to be talking about scatter diagrams scatter diagrams are also known as Scatter Plots or scatter charts those terms are used interchangeably in essence what we're doing is we're plotting two variables against each other on a graph to look for a relationship between those variables so to use a scatter plot we're trying to think are two variables related we plot those variable coordinates on a graph and then we look for Trends and possible correlation between those variables so let's see what a couple of these plots look like here we have one on the left that shows a relationship between car weight and gas mileage the weight of the car is being represented by the xaxis and the Y AIS represents the gas mileage using XY coordinates for each car weight there's a corresponding gas mileage and it's plotted there on the chart and it looks kind of scattered and that's why it's called a scatter plot but even though they're kind of spread out we can see that there's some sort of relationship between them and that kind of looks like as the weight of a car increases the gas mileage will decrease the plot on the right is showing the relationship between the stopping dist distance of a vehicle and how fast it's traveling the speed is being shown on the xaxis the stopping distance on the Y AIS and just like with the car weight one we have little dots that are scattered across this chart for each vehicle speed with its stopping distance and again we can kind of see that there is a relationship between these two variables that this time as the speed increases so will the stopping distance to help us look at this a little better we can add trend lines these trend lines are linear lines that show a relationship between these two variables we don't expect the trend line to fit exactly to those dots but it does take all those dots into consideration and creates a linear line so what does all of this mean well if the trend line goes down it shows that there is a negative correlation between variables negative meaning as one variable increases the other one decreases so in the case of the car weight going up that means the gas mileage goes down the trend line going up means that there's a positive correlation between the variables which means as one variable increases so will the other one as the speed increased on the vehicle so did the stopping distance now there can be other possibilities there can be no correlation there can be cyclical there could be patterns there all sorts of things that can happen with Scatter Plots I just showed you a couple of them but how do we go about making a scatter plot well in Excel we would enter the data into two columns one representing the x coordinate and the other one representing the y-coordinate so in this case if we had a batch size and the number of defects we would have the batch Sid as one coordinate and defects as the other once that's in place we would select the XY or scatter plot from chart tools and it would create the chart for us and then we can edit it to add the access titles and you can see those data points sitting there on the chart then we would add a trend line or in addition to that we can add the r s which is the coefficient of determination and that trend line typically we'll start with a linear Trend that's the default and that shows how that relationship works so in this case as batch size increases so will the number of defects it's a positive line going upwards and so we have a positive relationship between those two variables when we look at the r s the coefficient of determination It Must Fall between zero and one and the higher the value it indicates that that trend line that we added explains the relationship between the variables we can also look at the correlation coefficient which is R which is also known as the square root of the coefficient of determination the greater the value of R the stronger the relationship is between those two variables so we consider it's strong if it's greater than 08 and if it's less than 0.5 we consider it weak so that's all there is to Scatter Plots we are looking looking at a relationship between two variables and seeing what that relationship is and I'll see you next time when we look at another one of those seven tools of quality take care