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Published byMadeline Pollock Modified about 1 year ago

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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:

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I’m 18 and I spent £25 Age1816 Amount2510 I’m 16 and I spent £10

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Age Amount I’m 18 and I spent £10 I’m 17 and I spent £22 I’m 15 and I spent £8

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Age Amount I’m 17 and I spent £15 I’m 19 and I spent £30

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Age x Amount y This graph needs to be rescaled.

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Age Amount This graph is clearer due to a better scale.

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This line is called the line of best fit. If it goes up in this direction, it has a positive correlation.

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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

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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

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Drawing the line of best fit. The line of best fit must pass through the: Mean x value and the mean y value

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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 =

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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 =

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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

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Drawing the line of best fit. If the data is plotted using EXCEL then the value of r can be obtained

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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

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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?

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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.

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