GCSE Statistics practice, marked as they go.

1. 1Types of Data+

   • Recognise that data can be obtained from primary and secondary sources
   • Recognise the difference between quantitative and qualitative variables
   • Recognise the difference between discrete and continuous data
   • Recognise and use scales of measurement: categorical, rank, ordinal
   • Categorise data through the use of well-defined, precise definitions or class boundaries
   • Understand, use and define situations for grouped and ungrouped data
   • Understand the meaning of bivariate data and multivariate data
   • Know the difference between independent and dependent variables
2. 2Population and Sampling+

   • Understand the meaning of the terms population and sample
   • Understand the word 'census' with regard to small scale and large scale populations
   • Understand the reasons for sampling and that sample data is used to estimate values in a population
   • Understand that sample size has an impact on reliability and replication
   • Understand, design and use a sampling frame
   • Apply and use Peterson's data capture technique to estimate population sizes and know the assumptions made
3. 3Sampling Methods+

   • Understand the terms random, randomness and random sample
   • Understand the use of random numbers and some of the methods of generating these: random number tables, the random number function on the calculator, picking random numbers from a hat
   • Be able to select a random sample, or a stratified sample, by one category as a method of investigating a population
   • Appreciate how bias in a sampling procedure might occur and how it might be minimised
   • Know the difference between opportunity (convenience), systematic, quota, judgement and stratified sampling (stratified could be by more than one category)
4. 4Planning and Collecting Data+

   • Understand that there are different methods to collect primary data from different sources
   • Identify appropriate sources of secondary data
   • Extract data from secondary sources, including those based on ICT
   • Understand that data needs to be 'cleaned' before being used
   • Understand the aspects of accuracy, reliability, relevance and bias as related to secondary data
   • Know the purpose of pilot surveys
   • Know how random response is used for sensitive questions
   • Understand the techniques used to deal with possible problems associated with the collection of data (including issues of sensitivity)
   • Understand why control groups are used in questioning and testing, and the system of matched pairs to avoid bias
   • Form a hypothesis, and know the appropriate strategies to test this hypothesis
   • Be aware of factors involved with testing a hypothesis (including time, costs, ethical issues, confidentiality and convenience)
   • Identify problems that may arise with the statistical enquiry cycle (e.g. non-response of surveys, difficulty estimating the population or unexpected outcomes) and come up with strategies to help overcome these
5. 5Correlation+

   • Plot points as points on a scatter diagram
   • Recognise positive, negative and zero correlation by inspection
   • Understand the distinction between correlation and causality
   • Draw a line of best fit through (x̄, ȳ) to the points on a scatter diagram and find the equation of the regression line
   • Understand the pitfalls of interpolation and extrapolation
   • Interpret data presented in the form of a scatter diagram
   • Calculate and interpret Spearman's rank correlation coefficient
   • Interpret Pearson's product moment correlation coefficient
   • Understand the distinction between Spearman's and Pearson's correlation coefficients
   • Know and apply the words: positive, negative, zero, causation, association, interpolation, extrapolation, independent variable, explanatory variable, response variable, dependent variable
   • Describe and make comparisons of the strength of correlation
6. 6Moving Averages+

   • Plot points as a time series
   • Draw a trend line by eye and use it to make a prediction
   • Interpret seasonal and cyclic trends in context
   • Calculate and use a 4 point moving average or other specified appropriate moving average
   • Find the mean seasonal variation and extrapolate the data to make predictions for future years
7. 7Index Numbers+

   • Have an understanding of the retail price index (RPI), consumer price index (CPI) and gross domestic product (GDP) and other index numbers in context
   • Calculate and interpret simple index numbers
   • Calculate and interpret rates of change over time including, but not limited to, births, deaths, house prices, unemployment and percentage change
8. 8Probability+

   • Calculate estimates of probabilities and represent these as a fraction, decimal or percentage
   • Interpret probability values
   • Understand the meaning of the words 'impossible', 'certain', 'highly likely', 'likely', 'unlikely', 'possible', 'evens', and present them on a likelihood and number scale
   • Compare expected frequencies and actual frequencies
   • Recognise that experimental probability will tend towards theoretical probability as the number of trials increases
   • Identify bias if experimental probability does not tend towards theoretical probability
   • Know and apply formulae for conditional probability and independent events
   • Use collected data and calculated probabilities to determine and interpret relative risks and absolute risks, and express in terms of expected frequencies in groups
   • Comment on the differences between experimental and theoretical values in terms of possible bias
   • Produce, understand and use a sample space
   • Understand the terms mutually exclusive and exhaustive and understand the addition law P(A or B) = P(A) + P(B) for two mutually exclusive events
   • Draw and use probability tree diagrams for independent events (at most three events)
   • Use Venn diagrams and two-way tables to represent all possible outcomes
   • Understand, use and apply the addition law for mutually exclusive events, and the multiplication law for independent events
   • Calculate conditional probability following a tree diagram, two-way table or Venn diagram
9. 9Discrete Data+

   • Construct, draw, use and understand: pictograms, bar charts, multiple or composite bar charts for qualitative and discrete data, vertical line graphs, stem and leaf diagrams, Venn diagrams
   • Understand the distinction between well-presented and poorly presented data
   • Understand the potential for visual misuse, by omission or misrepresentation
   • Transform from one presentation to another
   • Understand how to discover errors in data and recognise data that does not fit a general trend or pattern
   • Use comparative 2D and 3D representations
   • Group data into class intervals and be aware of the advantages and implications of doing so
10. 10Continuous Data+

    • Construct, draw, use and understand: pie charts, histograms with equal and unequal class intervals, frequency polygons, cumulative frequency diagrams, population pyramids, choropleth maps, box plots
    • Transform from one presentation to another
    • Understand how to discover errors in data and recognise data that does not fit a general trend or pattern
    • Group data into class intervals and be aware of the advantages and implications of doing so
    • Use calculated or given summary statistics for continuous data to make estimates of population characteristics, for example samples to estimate the population mean
11. 11Tabulation+

    • Construct, draw, use and understand two-way tables and tally charts, and any other data represented in a table format
12. 12Central Tendency+

    • Calculate the mean, mode and median for a list of numbers
    • Calculate the mean, mode and median for discrete data listed in a table (grouped)
    • Calculate the mean, mode and median for continuous data listed in a table (grouped), including linear interpolation for the median
    • Understand the appropriateness, advantages and disadvantages of each of the three measures of central tendency
    • Understand the effect of transformations on the mean, mode, median
    • Calculate the geometric mean and weighted mean
13. 13Dispersion+

    • Calculate the range, quartiles, percentiles and interquartile range for discrete and continuous data
    • Calculate the interpercentile range and interdecile range
    • Calculate the standard deviation
    • Compare data samples, and compare sample data with population data when given measures of dispersion
14. 14Box Plots and Skewness+

    • Construct, interpret and use box plots from summary statistics
    • Construct, interpret and use box plots from cumulative frequency graphs
    • Calculate outliers using the formulae: a small outlier is < LQ − 1.5 × IQR, a large outlier is > UQ + 1.5 × IQR, or an outlier is outside µ ± 3σ
    • Show outliers on box plots and comment with reference to the original data
    • Determine skewness by inspection and calculation
    • Make interpretations in context
    • Use box plots as a method to compare two (or more) sets of data for dispersion, measure of central tendency and skewness
    • Identify simple properties of the shape of distributions of data including symmetry, positive and negative skew
15. 15Binomial+

    • Understand the notation B(n, p)
    • Identify when a binomial distribution should be used and the conditions needed
    • Calculate probabilities using any standard method including use of a calculator
    • Know the calculation for the mean of a binomial distribution is np
    • Know the properties of the binomial distribution
16. 16Normal+

    • Know the shape of a normal distribution curve and how this occurs
    • Understand the notation N(µ, σ²)
    • Know the conditions that make the normal distribution model suitable
    • Know that 68% of data lies within one standard deviation of the mean, and 95% of data lies within two standard deviations of the mean
    • Know how to draw two distribution curves on the same graph
    • Use standardised scores to compare two samples of data
17. 17Quality Assurance+

    • Understand the process of quality assurance and see why this is necessary in the real world
    • Know how to calculate both warning limits and action limits
    • Know how to draw warning limits and action limits on a sample mean, median or range versus sample number graph
    • Understand how action and warning limits are used in the manufacturing process

Topics follow the AQA 8382 specification. PrepAcer is independent and not affiliated with the exam board.