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Mr F’s Maths Notes Statistics 8. Scatter Diagrams

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Why do we bother with Statistical Diagrams? The answer to this question is similar to the one for: “why do we bother working out averages and measures of spread?”. We live in a world jam-packed full of statistics, and if we were forced to look at all the facts and figures in their raw, untreated form, not only would we probably not be able to make any sense out of them, but there is also a very good chance our heads would explode. Statistical Diagrams – if they are done properly - present those figures in a clear, concise, visually pleasing way, allowing us to make some sense out of the figures, summarise them, and compare them to other sets of data. 1. Drawing the Correct Scale It never ceases to amaze (or depress) me just how many people get everything else correct when drawing a statistical diagram, but mess up their scale and lose loads of marks! Remember: When choosing a scale, make sure you always go up in equal steps along each axes! Here are some examples of some really dodgy scales. See if you can tell what is wrong with each… and make sure you never make the same mistake!

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Example 1Example 2

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Example 3 Example 4

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The Answers 1)This person has messed up their negative numbers. Remember, scales must go from smallest to biggest, from left to right, and down to up. 2) Classic mistake. Numbers must go on the lines, not between the spaces! 3)How many times have I seen this? The spaces around the centre (origin) are not equal. Look at the gap between 2 and – 2…. Deary me! 4)Inconsistent scales! Notice the numbers go up by 1 in the negatives and then 2 in the positives! Note: Another mistake in all of the diagrams is that the x and y axes are not labelled! Big Example Below is a table showing the number of pupils who fail to hand in their maths homework each day, and the minutes of yoga I need to do to calm myself down Draw a scatter diagram to show the information, add a line of best fit, and comment on the correlation Pupils missing homework 35210204815614 Minutes of yoga101292583152026107

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2. Drawing a Scatter Diagram 1. Decide on an appropriate scale that will look a decent size and fit all the data in! Note: It doesn’t really matter which set of data goes on the x axis and which on the y… but personally I like to put the one with the biggest numbers on the y axis! BUT: remember to label both axes, including units! 2. Carefully mark each piece of data on your diagram with a dot/cross, and when you have finished, check you have the correct number of crosses!

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3. The Line of Best Fit This is a single straight line which is supposed to be a good representation of the pattern / trend of the data Tips for drawing it: Try to get roughly the same amount of points above the line as below Experiment by using your ruler as your line, and only draw the line in when you are happy Don’t spend too long deciding, and don’t try to make it perfect! Note: Your line does NOT have to start at the origin (0, 0)

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4. Correlation The most important use of scatter diagrams is to determine the type (if any) of correlation between two variables Correlation is just a posh word for relationship. There are two categories of correlation that you need to be familiar with: DIRECTION Positive – line slopes upwards As one variable increases, so does the other Negative – line slopes downwards As one variable increases, the other decreases No correlation – line is close to horizontal No relationship between the variables STRENGTH Strong – dots are close to each other Weak – dots are far apart Tip: When deciding on the strength of correlation, I have a little rule: “the longer it takes me to decide where to draw the line of best fit, the weaker the correlation” Looking at our example, I would say there is a fairly strong, positive correlation. This is no surprise, because as the number of missing homeworks increases, so to does my need for yoga! Strong negative Weak PositiveNo Correlation

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5. Using your Line of Best Fit Once we have drawn our line of best fit, we can use it to predict results we don’t already have Note: The stronger the correlation, the more reliable these predictions will be! Question 1: If 7 pupils forget to hand in their homework, how many minutes of yoga might Mr Barton do? Question 2: If Mr Barton does 28 minutes of yoga, how many pupils might have forgotten their homework? Following the red line up and across gives… 16 minutes Following the purple line across and down… 14.5 pupils

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Good luck with your revision!

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