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AS and A Level: Probability & Statistics

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Statistical diagrams

  1. 1 When working with grouped data, if the class is from 9 to 12, this includes values from 8.5 up to 12.5, which means the class width is 4, not 3.
  2. 2 In a histogram, the area is the frequency. The y-axis is the frequency density.
  3. 3 When working out lengths of scaled histograms, it is always helpful to draw the rectangle and label the relevant sides with the lengths given.
  4. 4 When drawing a stem and leaf diagram, make sure to include a key. The key is worth a mark. For example 2|1 represents 2.1 or on a different stem and leaf, 3|2 represents 32.
  5. 5 Always draw a scale when drawing a box plot, the scale is worth a mark.

How to tackle questions on regression and correlation

  1. 1 When asked about the relationship in a regression model, always get the context the correct way round. For example, weight does not affect height, height effects weight.
  2. 2 When asked if your answer is reliable for the regression model, comment on whether the x value you used to get the answer is within the original data set. If the x value is within the boundary it is suitable. Never extrapolate when using a regression model.
  3. 3 If you have found a regression model for a relationship between h and p, and are then told h=x+100 and p=y-20 and asked to find a regression model for x and y. Sub x+100 and y-20 into your original equation and re-arrange.
  4. 4 When data is coded the correlation co-efficient is not changed.
  5. 5 If a regression model is created using for example, heights and weights of children. This model could not be used to predict the weight of an adult. Models are very specific to the data with which they were created..

Normal distribution

  1. 1 When answering normal distribution questions always draw a picture and shade in the part of the graph that you know and/or want.
  2. 2 In a normal distribution, the area under the curve represents the probability.
  3. 3 A normal distribution model is appropriate if the mean and median are the same, or very close.
  4. 4 The big normal distribution table gives area to the left of the line. The small table has areas to the right of the line.
  5. 5 If unsure what the question is asking. Do the first step which is to rewrite the question, but converted to the normal distribution.

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  1. Mathematically Modelling Basketball Shots

    This is impossible to create so the coursework will have to involve sampling, therefore not producing results representative of the whole population. For this coursework I can not take random samples because it will not be possible to recreate due to the infinite choices of shot which could occur e.g. fatigue levels, mood type, improvement of skill level throughout the sampling etc. all could differ. I will record a sample of X by asking Lee to shoot a number of baskets and hence work out the relative frequency of success - 'p'.

    • Word count: 2977

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