Presentation on theme: "Scattergrams A scattergram a type of graph that is used to try to find a relationship between two variables (things) Here is an example of how the information."— Presentation transcript:
Scattergrams A scattergram a type of graph that is used to try to find a relationship between two variables (things) Here is an example of how the information about AGE and AMOUNT OF MONEY SPENT AT THE WEEKEND is put onto a scattergram. People were asked: What is your age? How much money did you spend this weekend? Their answers were recorded in a table like this:
I’m 18 and I spent £25 Age1816 Amount2510 I’m 16 and I spent £10
Age Amount I’m 18 and I spent £10 I’m 17 and I spent £22 I’m 15 and I spent £8
Age Amount I’m 17 and I spent £15 I’m 19 and I spent £30
Age x Amount y This graph needs to be rescaled.
Age Amount This graph is clearer due to a better scale.
This line is called the line of best fit. If it goes up in this direction, it has a positive correlation.
click on hyperlink above To measure the correlation a value r is calculated which lies between –1 and +1. This is called the correlation coefficient If all the points lie on a perfect straight line then r equals either +1 or –1. If the points are totally scattered and there appears to be no line of best fit then r = 0. Other values of r indicate a degree of correlation – strong, medium or weak. Types of Correlation
Perfect positive correlation r = 1 Moderate positive correlation r = 0.6 Very weak positive correlation r = 0.1 No correlation r = 0 Quite strong negative correlation r = –0.7 Perfect negative correlation r = –1
Drawing the line of best fit. The line of best fit must pass through the: Mean x value and the mean y value
Finding the mean x and y value Age x Amount y To find the mean x value add up all the ages and divide by how many there are Total age = = 120 Number of values = 7 Mean Age =
Finding the mean x and y value Age x Amount y To find the mean y value add up all the money and divide by how many there are Total age = = 120 Number of values = 7 Mean Age =
Drawing the line of best fit. The line of best fit must pass through the point (17.1, 17.1) The mean x and y values are not usually the same
Drawing the line of best fit. If the data is plotted using EXCEL then the value of r can be obtained
Using the handout on using Excel follow the stages to plot the scatter diagram and draw the line of best fit with the correlation coefficient r
1.Plot these points on a scattergram. PupilABCDEFGHIJKLM Shoe S Height a. What type of correlation does the scattergram show between shoe size and height? b. What can you usually say about the connection between shoe size and height?
Plot these points on a scattergram to show the connection between revision and number of GCSE passes. PupilABCDEFGHIJKL Hours Rev No. GCSE a.What type of correlation does this show b.Draw a line of best fit onto the scattergram after having determined the mean x and the mean y value. c.Use this line to estimate how many hours are needed for 7 GCSE passes.