• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

AS and A Level: Probability & Statistics

Browse by

Currently browsing by:

4 star+ (1)
3 star+ (1)

Meet our team of inspirational teachers

find out about the team

Get help from 80+ teachers and hundreds of thousands of student written documents

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.

  1. 1
  2. 2
  1. I have been given the task of finding what affects the price of a used car, using a spreadsheet given to me displaying data on a hundred cars with data on about each car.

    It then dawned one me that I could use the depreciation price, the price when I took the used price away from the new, this perhaps could be a more accurate look at the data as some cars depreciate quicker than others. Looking further into that work I decided against it as it would take longer and time was of the essence, but this was perhaps an extension that could be added on at the end. Reasons Why * Age: Has a large range and would be interesting to see what sort of relationship there is * Insurance Group: Again a wide range.

    • Word count: 2263
  2. Study of the height/diameter ratio of limpets inhabiting the middle shore region of exposed and sheltered shores

    in order to resist wave attack and predators. When the tide rises and covers these molluscs, they move around and feed on algae before returning to their rock scar. Limpets have an opening underneath the shell where a muscular foot attaches the mollusc to the rock by means of suction and glue like adhesion. The clamping down also prevents them from desiccation. Water is drawn in through a hole above the head; gills will then be used for gaseous exchange. They will most commonly be found in the middle shore, this being the reason why we performed the study in the latter part of the shoreline.

    • Word count: 2624
  3. I shall collect data from a population in order to estimate population parameters (e.g. and 2) by using estimating techniques.

    (According to the Central Limit Theorem). THE STATISTICAL THEORY Central Limit Theorem: i) If the sample size is large enough, the distribution of the sample mean is approximately Normal. ii) The variance of the distribution of the sample mean is equal to the variance of the sample mean divided by the sample size; ?2 n _ Symbolically if X~ (unknown)(�, ?2) then X n ~N �, ? 2 n These approximations get closer as the sample size, n gets bigger.

    • Word count: 2386
  4. Statistics: Survey of Beijing and China during the SARS storm

    As the capital of China, it had been developed to an international city. The biggest cultural and political center. Weather is cold and has a big population. But it is the biggest disaster area of China. Aim: � To investigate the relationship(distribution) of death number in March and April during the SARS storm in China mainland. � To investigate the direction of SARS trended. Hypothesis: � I predict the current of SARS started from Guangzhou, which is a southern city to Beijing , which is a northern city. At the prophase of the SARS storm, Guangdong is the factor effect the SARS tainted number of China.

    • Word count: 2212
  5. How Can Samples Describe Populations?

    To try and fulfil this rudimentary and salient criterion in investigation, sampling techniques have been developed and employed. Number of Samples When using samples and attempting to represent the view of a designated population, it is apparent that the data acquired from one member of the population is very unlikely to lead to any conclusions. The law of averages suggests that the greater the number of samples, the more accuracy the data will have. Therefore, it is better to include as many samples as possible, but how many samples are sufficient to justify findings?

    • Word count: 2969
  6. Investigating Growth in Stride Length During the Human Growth Stage

    Also the numbers of pupils in each year group are of very similar sizes so stratified sampling would not have been of any use. The sampling frame that I have chosen to be a representation of the population, is a class list arranged alphabetically for both years 7 and 12. YEAR 7 Total number of pupils= 150 Sample size= 30 150/30= 5 Random number from 1 to 5 on calculator= 2 I therefore chose every 5th member of the population starting from the student numbered 2 in the class list, e.g.

    • Word count: 2163
  7. 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

Marked by a teacher

This document has been marked by one of our great teachers. You can read the full teachers notes when you download the document.

Peer reviewed

This document has been reviewed by one of our specialist student essay reviewing squad. Read the full review on the document page.

Peer reviewed

This document has been reviewed by one of our specialist student document reviewing squad. Read the full review under the document preview on this page.