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Mathematics

Statistics

Statistics, which is used to gather, process and analyze data regarding a population,1 is a valuable decision-making tool in many fields. This branch of mathematics is based on concepts and processes related to probability, particularly as regards sampling.

In elementary school, students were introduced to descriptive statistics, which allowed them to summarize raw data in a clear and reliable way. They conducted surveys, i.e. they learned how to formulate questions, gather data and organize it using tables, and interpreted and displayed data using bar graphs, pictographs and broken-line graphs. They also obtained relevant information using circle graphs, and calculated and interpreted the arithmetic mean of a distribution.

In Secondary Cycle One, students carry out studies using sample surveys and censuses. They acquire the tools they need to process the data they may or may not have gathered and extract information from these data. They learn about circle graphs as a possible method of data representation. They choose the graph(s) that will best illustrate a situation. They learn to highlight information such as minimum value, maximum value, range and mean and look for potential sources of bias.

In Secondary Cycle Two, descriptive statistics is used to introduce students to inferences. The situations dealt with allow students to gather, organize and represent data using the most appropriate graph, and determine certain statistical measures such as measures of central tendency, of position and of dispersion. They interpret data by observing their distribution (type, range, centre, groups), and check whether the distribution includes outliers that could influence certain measures or conclusions. They compare distributions, using appropriate measures of central tendency and of dispersion. They learn how to interpret a correlation qualitatively, using an approximate value of the correlation coefficient or quantitavely, by calculating its exact value using technological tools, if necessary.

The following tables present the learning content associated with statistics. By basing themselves on the concepts and processes targeted, students develop the three competencies of the program, which in turn enable students to better integrate the mathematical concepts and processes presented.

Analyzing and making decisions about one- or two-variable distributions,
using statistical tools		  
Student constructs knowledge with teacher guidance.
Student applies knowledge by the end of the school year.
 
Student reinvests knowledge.
Secondary
Cycle
One		 Cycle
Two
  1. One-variable distributions
 6 1 2 3 4 5
  1. Conducts a survey or a census
    1. Formulates questions for a survey
      Note : The questions become more refined over the years.
           CST
    TS
    S
    1. Chooses a sampling method :
  
      1. simple random, systematic
          
      1. stratified, cluster
           CST
    TS
    S
    1. Chooses a representative sample
          
    1. Collects, describes and organizes data (classifies or categorizes) using tables
           CST
    TS
    S
  1. Recognizes possible sources of bias
    Note : In CST in Secondary IV, students learn to correct the source of bias, if applicable.
         
  1. Interprets data presented in a table or a bar graph, a pictograph, a broken-line graph or a circle graph
            
  1. Distinguishes different types of statistical variables: qualitative, discrete or continuous quantitative
          
  1. Chooses appropriate register(s) (types) of representation to organize, interpret and present data
              
  1. Organizes and presents data using
    1. a table, a bar graph, a pictograph and a broken-line graph
            
    1. a table presenting variables or frequencies, or using a circular graph
          
    1. a table of condensed data or data grouped into classes, a histogram, or box-and-whisker plot
          CST
    TS
    S
    1. a stem-and-leaf diagram
           CST
    TS
    S
  1. Compares one-variable distributions
          
  1. Understands and calculates the arithmetic mean
           
  1. Describes the concept of arithmetic mean (levelling or balance point)
         
  1. Calculates and interprets an arithmetic mean
    Note : In Secondary Cycle One, the arithmetic mean is calculated using positive or negative numbers written in decimal or fractional notation.
          
  1. Determines and interprets
 
    1. measures of central tendency: mode, median, weighted mean
            
    1. measures of dispersion :
      1. range
         
      1. range of each part of a box-and whisker plot, interquartile range
            
      1. mean deviation
           CST
  TS
    S
      1. standard deviation
             CST
  TS
    S
    1. measures of position :
      1. minimum, maximum
          
      1. percentile
        Note : Percentile is determined using a sufficient number of data. Students can also determine corresponding data from a percentile.
           CST
    TS
    S
  1. Chooses the appropriate statistical measures for a given situation
        CST
    TS
    S
  1. Two-variable distributions
6 1 2 3 4 5  
  1. Compares experimental and theoretical data
    Note : In Secondary III, the study of linear and rational functions is introduced through the use of scatter plots.
            
  1. Represents data using a scatter plot or a double-entry (two-variable) distribution table
           
  1. Associates the most appropriate functional model with a scatter plot :
 
    1. first-degree polynomial function
           CST
  TS
  S
    1. functions under study
      Note : In TS, technological tools should be used for models that are not linear.
             CST
  TS
    S
  1. Describes and interprets the relationship between two variables, if any
           
  1. Gives a qualitative assessment of a linear correlation
    Note : In TS, qualitative assessment should be used for nonlinear models.
           
  1. Approximates and interprets the linear correlation coefficient
    Note : If necessary, technological tools can be used to determine the value of the correlation coefficient for the models under study.
            
  1. Draws a curve associated with the chosen model
    Note : In Secondary V, scatter plots are studied with functions.
           CST
  TS
  S
  1. Represents a regression line algebraically or graphically
    Note : In addition to drawing this line freehand, students may use other methods, such as the median-median line or the Mayer line method.
           
  1. Interpolates or extrapolates values using
    1. a regression line
           CST
  TS
  S
    1. the functional model best suited to the situation
            CST
  TS
  S
  1. Compares two-variable distributions
           CST
  TS
  S
1.  A population is a set of entities (e.g. individuals of a species, facts) included in a statistical study.

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