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:
1ScattergramsA 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:
2I’m 16 and I spent £10I’m 18 and I spent £25Age1816Amount2510
3Age 18 16 17 15 Amount 25 10 22 8 I’m 17 and I spent £22
4Age 18 16 17 15 19 Amount 25 10 22 8 30 I’m 17 and I spent £15
5Age x1816171519Amount y251022830This graph needs to be rescaled.
6Age1816171519Amount251022830This graph is clearer due to a better scale.
7This line is called the line of best fit. If it goes up in this direction, it has a positive correlation.
8Types of Correlationclick on hyperlink above To measure the correlation a value r is calculated which lies between –1 and +1. This is called the correlation coefficientIf 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.
9r = 1 r = 0.6 r = 0.1 r = 0 r = –0.7 r = –1 Perfect positive correlationr = 1Moderate positive correlationr = 0.6Very weak positive correlationr = 0.1No correlationr = 0Quite strongnegative correlationr = –0.7Perfect negativecorrelationr = –1
10Drawing the line of best fit. The line of best fit must pass through the:Mean x value and the mean y value
11Finding the mean x and y value Age x1816171519Amount y251022830To find the mean x value add up all the ages and divide by how many there areTotal age = = 120Number of values = 7Mean Age =
12Finding the mean x and y value Age x1816171519Amount y251022830To find the mean y value add up all the money and divide by how many there areTotal age = = 120Number of values = 7Mean Age =
13Drawing 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
14Drawing the line of best fit. If the data is plotted using EXCEL then the value of r can be obtained
15Using 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
16Plot these points on a scattergram. PupilABCDEFGHIJKLMShoe S.234576Height184.108.40.206.81.71.6What type of correlation does the scattergram show between shoe size and height?What can you usually say about the connection between shoe size and height?
17What type of correlation does this show Plot these points on a scattergram to show the connection between revision and number of GCSE passes.PupilABCDEFGHIJKLHours Rev.456797345781249768990No. GCSE46912810What type of correlation does this showDraw a line of best fit onto the scattergram after having determined the mean x and the mean y value.Use this line to estimate how many hours are needed for 7 GCSE passes.