The following techniques should be introduced as soon as possible and used throughout the course:
• using statistical terms correctly eg qualitative and quantitative data, primary and secondary data, independent and dependent variables, discrete and continuous variables, population, representative and random samples, outliers.
• using spreadsheets to carry out calculations and display results in tables and statistical charts and graphs
• checking calculations using estimates, inverse operations and different methods.
Although the topics are listed separately below, it would be more beneficial to follow a number of statistical investigations through from the initial collection and organisation of data to an analysis of the situation making use of statistical charts and measures. Where possible these investigations should reflect the students’ other areas of work and interests.
Note that topics given below as Extension Opportunities are optional, but students must do some work outside the main core in their coursework portfolio.
Carrying Out Investigations
Identify characteristics that are pertinent to investigations. Use statistical terms - qualitative and quantitative data, primary and secondary data, discrete and continuous variables, population, representative, biased, random and stratified samples etc.
Discuss different methods of collecting data – the use of surveys (including questionnaires), observations and experiments. Include ideas associated with consistency, repeatability and variability between samples.
MUSIC- Students write an hypothesis and design an experiment to test whether listening to music has any effect on the performance of people doing work. Includes arithmetic tests that may be used to carry out such an experiment.
DISCUSS Sampling Methods
DISCUSS Worksheet
CENSUS AT SCHOOL ACTIVITIES
Discuss different methods of collecting data – the use of surveys (including questionnaires), observations and experiments. Include ideas associated with consistency, repeatability and variability between samples.
MUSIC- Students write an hypothesis and design an experiment to test whether listening to music has any effect on the performance of people doing work. Includes arithmetic tests that may be used to carry out such an experiment.
DISCUSS Sampling Methods
DISCUSS Worksheet
CENSUS AT SCHOOL ACTIVITIES
Statistical Charts
Drawing and interpreting bar charts (include comparative and component bar charts), pie charts (including comparative pie charts) line graphs and histograms.
Using a spreadsheet to draw charts and graphs.
Describe the shape of distributions using terms such as symmetrical, skewed, multi-modal.
Interpreting complex charts eg line graph superimposed on bar chart and any charts or graphs related to students’ other studies.
Extension Opportunities – other appropriate diagrams eg stem & leaf.
Histogram Cut Up MSV 1 MSV1 Answer
Using a spreadsheet to draw charts and graphs.
Describe the shape of distributions using terms such as symmetrical, skewed, multi-modal.
Interpreting complex charts eg line graph superimposed on bar chart and any charts or graphs related to students’ other studies.
Extension Opportunities – other appropriate diagrams eg stem & leaf.
Histogram Cut Up MSV 1 MSV1 Answer
Statistical Measures
Find mean, mode, median, range, quartiles and standard deviation of data from a list and from a frequency table. Consider outliers and include using both a calculator and spreadsheet.
Use of a cumulative frequency graph to find the median, quartiles and percentiles.
Compare and contrast data sets using statistical charts and measures.
Extension Opportunity – box & whisker.
Outlier tester MVS 4
Mean and Variance MSV 6 MSV 6 Answer
Use of a cumulative frequency graph to find the median, quartiles and percentiles.
Compare and contrast data sets using statistical charts and measures.
Extension Opportunity – box & whisker.
Outlier tester MVS 4
Mean and Variance MSV 6 MSV 6 Answer
Finding Information from Complex tables: Percentages and Reverse Percentage
Include calculation of percentages and ‘reverse’ percentages
Percentages Revision - Grade C GCSE kangaroomaths.co.uk
Percentages Revision - Grade C GCSE kangaroomaths.co.uk
Correlation and Regression
Definition of independent and dependent (controlled and response) variables.
Plot scatter diagrams of bivariate data, including the mean point and draw a line of best fit by eye. Understand positive, negative, strong, weak and no correlation.
Calculation and interpretation of the product-moment correlation coefficient (using both a calculator and spreadsheet).
Include the fact that correlation does not necessarily imply cause and effect, that a third variable may underlie correlation and that not all relationships are linear.
Discuss the principle of least squares. Find the equation of a regression line using both a calculator and spreadsheet. Draw the regression line (by hand and spreadsheet) and interpret regression coefficients in context.
Extension Opportunity – rank correlation coefficients, non-linear models.
DISCUSS Correlation and Regression Activity
DISCUSS Worksheet
Plot scatter diagrams of bivariate data, including the mean point and draw a line of best fit by eye. Understand positive, negative, strong, weak and no correlation.
Calculation and interpretation of the product-moment correlation coefficient (using both a calculator and spreadsheet).
Include the fact that correlation does not necessarily imply cause and effect, that a third variable may underlie correlation and that not all relationships are linear.
Discuss the principle of least squares. Find the equation of a regression line using both a calculator and spreadsheet. Draw the regression line (by hand and spreadsheet) and interpret regression coefficients in context.
Extension Opportunity – rank correlation coefficients, non-linear models.
DISCUSS Correlation and Regression Activity
DISCUSS Worksheet
The Normal Distribution
The use of theoretical probability distributions to model populations.
Features of normal distributions:
• continuous variable
• unimodal
• symmetrical
• mean = mode = median
• approximately two-thirds of the distribution lies within one standard deviation of the mean
• approximately 95% of the distribution lies within two standard deviations of the mean
The standard normal distribution with mean 0 and variance 1.
Use of the standard normal table to find probabilities and expected frequencies.
Use of the standard normal table in reverse calculations.
Extension Opportunities – other probability distributions eg uniform, binomial, Poisson.
Significance tests – t, z, Mann Whitney, Wilcoxin signed rank, chi-squared.
Chi Squared Test and Percentages
Hypothesis Testing MSV 15 MSV 15 Answers
Hypothesis Testing Tutorial
Features of normal distributions:
• continuous variable
• unimodal
• symmetrical
• mean = mode = median
• approximately two-thirds of the distribution lies within one standard deviation of the mean
• approximately 95% of the distribution lies within two standard deviations of the mean
The standard normal distribution with mean 0 and variance 1.
Use of the standard normal table to find probabilities and expected frequencies.
Use of the standard normal table in reverse calculations.
Extension Opportunities – other probability distributions eg uniform, binomial, Poisson.
Significance tests – t, z, Mann Whitney, Wilcoxin signed rank, chi-squared.
Chi Squared Test and Percentages
Hypothesis Testing MSV 15 MSV 15 Answers
Hypothesis Testing Tutorial
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