These lessons will involve the students in investigating and understanding:
The concept of a distribution of data and frequency distribution tables
MIS: Grouped Frequency Distribution
MIS: Normal Distribution
MIS: Skewed Distribution
OnlineStatBook: Detailed look at distributions in data
Khan Academy
Practice: Shape of distributions
Practice: Clusters, gaps, peaks, & outliers
The selection and use of appropriate graphical and numerical methods to describe the sample (univariate data only)taking account of data type: bar charts, pie charts, line plots, histograms(equal class intervals), stem and leaf plots (including back to back),
Presenting numerical data in tables & graphs
PM: Statistical Investigation: includes which graph to use with different data types
MIS: Bar Graph or a Pie Chart using the Data Graphs (Bar, Line and Pie), Histograms, Stem and Leaf Plots, extra (box & whisker plot)
Khan Academy
Practice: Read bar graphs and solve 2 step problems
Practice: Reading dot plots & frequency tables
Practice: Reading stem and leaf plots
Practice: Comparing data displays
The distribution of numerical data in terms of shape (concepts of symmetry, clustering, gaps, skewness)
Khan Academy
Practice: Shape of distributions
Practice: Clusters, gaps, peaks, & outliers
The selection and use of appropriate numerical methods to describe the sample
o The distribution of data in terms of centre (mean, median, mode and the advantages and disadvantages of each)
Khan Academy
Practice: Mean, median, and mode
Practice: Effects of shifting, adding, & removing a data point
Choosing the "best" measure of center
o The relative positions of mean and median in symmetric and skewed data
Relationships Between Mean, Median and Mode in Special Distributions
o The distribution of numerical data in terms of spread (range, inter-quartile range)
The concept of inter-quartile range as a measure of spread around the median
MIF: Interquartile Range
Khan Academy
Practice: Interquartile range (IQR)
Comparing range and interquartile range (IQR)
o The distribution of data in terms of spread (standard deviation)
The concept of standard deviation as a measure of spread around the mean
MIF: Standard Deviation
Khan Academy
The idea of spread and standard deviation
Calculating standard deviation step by step
Practice: Standard deviation of a population
The use of the calculator to calculator to calculate standard deviation
PM: How to set up your calculator
PM: Finding Statistics From Grouped Frequency Table on your Calculator
Analyse plots of data to explain differences in measures of centre and spread
KA: Center, spread, and shape of distributions — Basic example
Image showing relationship between shape and measure of spread
How to interpret a histogram in terms of distribution of data and make decisions based on the empirical rule (based on a normal distribution)
Document Showing various distributions
Outliers and their effect on measures of centre and spread
An overview of topics discussed
Use percentiles to assign relative standing
MIF: Percentiles
The effect on the mean of adding or subtracting a constant to each of the data points and of multiplying or dividing the data points by a constant