#Statistics #Year11 #Standard >[!info]- [Data analysis | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n11/fa4de413b8) >- MST-11-08 displays and analyses datasets using summary statistics and graphical representations ## 📖 Prior Knowledge | Content | Prior knowledge | Used for | | ----------------------------------------- | -------------------------------------------------------- | -------------------------------------------------------------------------- | | [[Data Classification and Visualisation]] | - classifying data<br>- creating and interpreting graphs | - *repeated content*<br>- grouped data | | [[Stage 4/Data Analysis\|Data Analysis]] | - surveys and samples<br>- summary statistics | - *repeated content*<br>- calculating summary statistics from grouped data | | [[Data Analysis A]] | - standard deviation<br>- box plots | - *repeated content*<br>- formal definition of an outlier | ## Statistical investigation process - Identify an issue and pose a question to a targeted population to gather statistical information - Develop a survey by applying questionnaire design principles of clear language, unambiguous questions and consideration of number of choices - Examine issues of privacy, bias, ethics and responsiveness to diverse groups and cultures ## Population and sample - Compare and contrast systematic sampling, self-selected sampling, random sampling and stratified sampling - Justify whether a sample obtained from a population is representative of the population by considering the sampling method - Describe the potential faults in the design and practicalities of a data collection process by considering survey design, experiments and observational studies, and misunderstandings and misrepresentations ## Data classification - Classify and describe variables as numerical or categorical - Describe a numerical variable as discrete or continuous - Describe a categorical variable as nominal or ordinal - Identify collections of data that can be described as numerical or categorical depending on responses ## Display and interpret grouped and ungrouped data - Recognise and explain why some datasets need to be grouped to allow for appropriate representation and analysis - Use a spreadsheet to organise and represent data using appropriate graphs - Represent a numerical dataset as either a frequency distribution table or a cumulative frequency distribution table and graph the associated histogram with polygon, both with and without using digital tools - Represent categorical datasets in tables and column graphs as appropriate, with and without using digital tools - Select the type of graph best suited to represent various single datasets and justify the choice of graph - Identify and describe the shape of the distribution of a dataset as either symmetric, positively skewed or negatively skewed - Interpret and analyse dot plots, line graphs, sector graphs, stem-and-leaf plots, back-to-back stem-and-leaf plots and divided bar charts related to real-world applications - Analyse a statistical infographic and justify the choice of graphical representations used for the relevant dataset - Interpret and consider limitations of graphical representations to make conclusions and predictions - Explain why a given graphical representation can lead to a misinterpretation of data ## Measures of centre and spread - Describe the mean, median and mode as measures of centre and calculate their values for a dataset in graphical form and tabular form, using a scientific calculator and other digital tools - Identify and describe datasets as uniform, unimodal, bimodal or multimodal - Identify the range and standard deviation as measures of spread to describe variation in a dataset - Calculate the range and population standard deviation  of a dataset using a scientific calculator or other digital tools - Compare datasets using measures of centre and measures of spread - Examine the merits of each measure of centre and justify where each measure is most appropriately used - Identify and describe real-world examples illustrating appropriate and inappropriate uses of measures of centre and measures of spread - Use a spreadsheet to analyse data including calculating measures of centre and spread ## Quartiles and interquartile range - Determine the five-number summary from a set of numerical data or graphical representation - Determine the interquartile range (IQR) of datasets - Compare and contrast the use of range and IQR as measures of spread ## Five-number summary and box plots - Represent numerical datasets using a box plot to display a five-number summary, with and without using digital tools - Compare and contrast the measures of centre, spread and shape using parallel box plots - Determine quartiles from datasets displayed in histograms and dot plots, and represent these datasets as a box plot - Interpret box plots to draw conclusions and make inferences about a dataset ## Clusters and outliers - Identify clusters, gaps and outliers and explain their occurrence in the context of the data - Apply $Q_1-1.5\times IQR$ and $Q_3+1.5\times IQR$  to formally identify outliers - Explain the impact of outliers on the measures of centre and spread