# Statistics

Complementing the study of Maths at GCSE, this GCSE Statistics course incorporates numerous examples of real-life data and contexts which build upon the skills the students learn in Maths but also in other subjects such as science and geography.

Students will gain a thorough and rounded understanding of how to interpret and apply data to a number of scenarios – across subjects and in the real world. Real-life statistical data and contexts will encourage students to really engage with the subject matter and help them to learn skills that transfer readily to other GCSE subjects and the work place.

Students are assessed across two papers. There is no assessed coursework.

The aims and objectives of this qualification are to enable students to develop statistical fluency and understanding through:-

- the use of statistical techniques in a variety of authentic investigations, using real-world data in contexts such as, but not limited to, populations, climate, sales etc.
- identifying trends through carrying out appropriate calculations and data visualisation techniques
- the application of statistical techniques across the curriculum, in subjects such as the sciences, social sciences, computing, geography, business and economics, and outside theclassroom in the world in general
- critically evaluating data, calculations and evaluations that would be commonlyencountered in their studies and in everyday life
- understanding how technology has enabled the collection, visualisation and analysis of large quantities of data to inform decision-making processes in public, commercial and academic sectors, including how technology can be used to generate diagrams and visualisations to represent data
- understand ways that data can be organised, processed and presented, including statistical measures to compare data, understanding the advantages of using technology to automate processing
- applying appropriate mathematical and statistical formulae, and building on prior knowledge.

The content itself follows the order of the traditional statistical enquiry code. By completing the qualification, students should be able to :-

- 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.
- Categorise data through the use of well-defined, precise definitions or class boundaries.
- Appreciate the implication of grouping for loss of accuracy in presentations.
- Understand, use and define situations for grouped and ungrouped data.
- Understand the meaning of bi-variate data which may be discrete, continuous, grouped or ungrouped.
- Understand the meaning of the term population.
- 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 the terms random, randomness and random sample.
- Understand the use of random numbers.
- Understand, design and use a sampling frame.
- Be able to select a random sample or stratified sample by one (and more than one) category as a method of investigating a population.
- Appreciate how bias in a sampling procedure might occur and how it might be minimised.
- Understand and use systematic, quota and cluster sampling.
- Understand the strengths and weaknesses of various sampling methods, including bias, influences and convenience.
- Collect or obtain data using a variety of methods
- Obtain primary data by questionnaires and experiments
- Understand the effects of accuracy on measurements.
- Understand the advantages and disadvantages of using interviews versus questionnaires.
- Design and use effective data capture sheets and methods of recording data.
- Understand the role, and use of pilot studies and pre-testing.
- Understand and account for the problems of design, ambiguity of wording, leading questions, definitions and obtaining truthful responses · Understand the advantages and disadvantages of open and closed questions.
- Be aware of the problems related to identifying the appropriate population, the distribution and collection of surveys, errors in recorded answers, non-response and missing data.
- Design simple statistical experiments to obtain data.
- Understand the need for identification of the variables to be investigated and the meaning of explanatory and response variables.
- Identify appropriate sources of secondary data.
- Extract data from secondary sources, including those based on ICT.
- Understand the aspects of accuracy, reliability, relevance and bias as related to secondary data.
- Understand surveys and the appropriateness of the conditions. Construct frequency tables by tallying raw data were appropriate, including open- ended class intervals and classes of varying width.
- Tabulate using class intervals for discrete and continuous data.
- Tabulate using various forms of grouping the data, including qualitative or quantitative categories.
- Combine categories to simplify tables with an understanding of the problems of over simplification, the effects on readability, the identification or masking of trends and the loss of detail.
- Problems associated with under and over simplification through inappropriate number of significant figures or an unsuitable group size.
- Read and interpret data presented in tabular or graphical form.
- Design suitable tables, including summary tables and two-way tables.
- Construct, draw, use and understand
- Pictograms
- Bar charts
- Multiple or composite bar charts for qualitative, quantitative and discrete data and comparative pie charts with area proportional to frequency
- Vertical line (stick) graphs for discrete data and cumulative frequency step polygons
- Stem and leaf diagrams
- Choropleth maps.
- Pie charts
- Histograms with equal and unequal class intervals and the concept of frequency density
- Frequency diagrams
- Cumulative frequency diagrams
- Population pyramids
- Stem and leaf diagrams.
- Identify simple properties of the shape of distributions of data including symmetry, positive and negative skew.
- Transform from one presentation to another.
- Understand that many populations can be modelled by the Normal distribution.
- Understand how to discover errors in data and recognise data that does not fit a general trend or pattern, including outliers.
- Convert raw data to summary statistics, design, construct and present summary tables.
- Work out the mean, median and mode of raw data presented as a list and as discrete data presented as a frequency distribution.
- Identify the modal class interval for grouped frequency distributions for discrete and continuous data.
- Work out and use estimates for the mean and median of grouped frequency distributions for discrete and continuous data.
- Understand the effects of transformations of the data on the mean, mode and median.
- Understand the effect on the mean, mode and median of changes in the data including the addition or withdrawal of a population or sample member.
- Understand the appropriateness, advantages and disadvantages of each of the three measures of central tendency.
- Be able to make a reasoned choice of a measure of central tendency appropriate to a particular line of enquiry, nature of data and purpose of the analysis.
- Calculate and use a weighted mean.
- Understand that increasing sample size generally leads to better estimates of population parameters.
- Estimate population means from samples.
- Estimate population proportions from samples with applications in opinion polls and elsewhere.
- Estimate population size based on the Peterson capture/recapture method.
- Understand the effect of sample size on estimates and the variability of estimates, with a simple quantitative appreciation of appropriate sample size.
- Convert raw data to summary statistics, design, construct and present summary tables.
- Work out and use the range for data presented in a list or frequency distribution.
- Work out the quartiles, percentiles and interquartile range for discrete and continuous data presented either as a list, frequency table or grouped frequency table.
- Construct, interpret and use box plots.
- Formally identify outliers.
- Calculate and use variance and standard deviation.
- Understand the advantages and disadvantages of each of the measures of dispersion, range, quartiles, interquartile range, percentiles, deciles, interpercentile range, variance and standard deviation.
- Use an appropriate measure of central tendency together with range, quartiles, interquartile range, percentiles, deciles, interpercentile range, variance and standard deviation to compare distributions of data.
- Calculate, interpret and use standardised scores to compare values from different distributions.
- Understand how to discover errors in data and recognise data that does not fit a general trend or pattern, including outliers.
- Plot points as points on a scatter diagram.
- Recognise positive, negative and zero correlation by inspection.
- Understand the distinction between correlation, causality and a non-linear relationship.
- Draw a line of best fit through to the points on a scatter diagram.
- Find the equation of the line of best fit in the form y = ax + b and a practical interpretation of a and b in the context.
- Fit non-linear models of the form y = axn + b and y = kax
- Understand the pitfalls of interpolation and extrapolation.
- Interpret data presented in the form of a scatter diagram.
- Calculate, in appropriate cases, Spearman’s rank correlation coefficient and use it as a measure of agreement or for comparisons of the degree of correlation.
- Plot points as a time series; draw a trend line by eye and use it to make a prediction.
- Calculate and use appropriate moving averages.
- Identify and discuss the significance of seasonal variation by inspection of time series graphs.
- Draw a trend line based on moving average.
- Recognise seasonal effect at a given data point and average seasonal effect.
- Understand the meaning of the words event and outcome
- Understand the meaning of the words impossible, certain, highly likely, likely, unlikely, possible, evens, and present them on a likelihood scale.
- Put outcomes in order in terms of probability.
- Put probabilities in order on a probability scale.
- Understand the terms random and equally likely.
- Understand and use measures of probability from a theoretical perspective and from a limiting frequency or experimental approach, and that increasing sample size generally leads to better estimates of probability.
- Understand that in some cases the measure of probability based on limiting frequency is the only viable measure.
- Compare expected frequencies and actual frequencies.
- Use simple cases of the binomial and discrete uniform distribution.
- Use simulation to estimate more complex probabilities.
- Use probability to assess risk.
- Produce, understand and use a sample space.
- Understand and use Venn diagrams and Cartesian grids.
- Understand the terms mutually exclusive and exhaustive and to understand the addition law P(A or B) = P(A) + P(B) for two mutually exclusive events.
- Know, for mutually exclusive outcomes, that the sum of probabilities is 1; and in particular the probability of something not happening is 1 minus the probability of it happening.
- Draw and use probability tree diagrams for independent events and conditional cases.
- Understand, use and apply the addition for mutually exclusive events, general addition, and multiplication laws for independent events and conditional events and outcomes.
- Understand and use simple index numbers.
- Understand and use chain base index numbers.
- Understand and use weighted index numbers.
- Understand and use the Retail Price Index (RPI).