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SOUTH AFRICAN QUALIFICATIONS AUTHORITY 
REGISTERED UNIT STANDARD THAT HAS PASSED THE END DATE: 

Use of probability to measure uncertainty 
SAQA US ID UNIT STANDARD TITLE
262537  Use of probability to measure uncertainty 
ORIGINATOR
SGB Statistics 
PRIMARY OR DELEGATED QUALITY ASSURANCE FUNCTIONARY
-  
FIELD SUBFIELD
Field 10 - Physical, Mathematical, Computer and Life Sciences Mathematical Sciences 
ABET BAND UNIT STANDARD TYPE PRE-2009 NQF LEVEL NQF LEVEL CREDITS
Undefined  Regular  Level 5  Level TBA: Pre-2009 was L5  8 
REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER
Passed the End Date -
Status was "Reregistered" 		 2018-07-01  2023-06-30  SAQA 06120/18 
LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT
2024-06-30   2027-06-30  

In all of the tables in this document, both the pre-2009 NQF Level and the NQF Level is shown. In the text (purpose statements, qualification rules, etc), any references to NQF Levels are to the pre-2009 levels unless specifically stated otherwise.  

This unit standard does not replace any other unit standard and is not replaced by any other unit standard. 

PURPOSE OF THE UNIT STANDARD 
The skills, values and knowledge reflected in this unit standard are required by people in the field of statistics. Learners should be able to contribute to a quality hierarchy of skills required to provide quality services in statistics by using probability to measure uncertainty.

A person credited with this unit standard is able to:
  • Explain different approaches used to define probability.
  • Use Venn diagrams to explain the laws of probability.
  • Calculate probability of events using the laws of probability.
  • Interpret probability contextually and explain the role of probability in life tables. 
    		•

    LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING 
  • Mathematics NQF Level 4.
  • Communication NQF Level 4. 
    		•

    UNIT STANDARD RANGE 
    N/A 

    Specific Outcomes and Assessment Criteria: 

    SPECIFIC OUTCOME 1 
    Explain different approaches used to define probability. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Historical perspectives of the approaches to probability are discussed to motivate the rationale behind the approaches. 

    ASSESSMENT CRITERION 2 
    Different conceptions of probability are discussed to show the strengths and weaknessess of each one of them. 

    ASSESSMENT CRITERION 3 
    The appropriate approaches to calculating probability are identified for a given context. 
    ASSESSMENT CRITERION RANGE 
    Appropriate approaches include classical and frequentist and subjective approaches.
     

    ASSESSMENT CRITERION 4 
    The concept of mutually exclusive events is distinguished from the concept of independent events in order to provide a firm foundation in probability. 

    SPECIFIC OUTCOME 2 
    Use Venn diagrams to explain the laws of probability. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The three axioms of probability are stated as the basic building blocks of the theory of probability. 

    ASSESSMENT CRITERION 2 
    The laws of probability are derived from the axioms using Venn diagrams. 

    ASSESSMENT CRITERION 3 
    The law of total probability is stated and justified using a Venn diagram. 

    SPECIFIC OUTCOME 3 
    Calculate probability of events using the laws of probability. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    Probabilities of unions and intersection of events are calculated for both independent and dependent events. 

    ASSESSMENT CRITERION 2 
    The law of total probability is used to calculate the probability of an event given a partitioning of the sample space. 

    ASSESSMENT CRITERION 3 
    Bayes' theorem is used to calculate conditional probability to solve problems on conditional events. 

    ASSESSMENT CRITERION 4 
    Appropriate probability law is selected to solve a specific problem. 

    ASSESSMENT CRITERION 5 
    The fundamental principle of counting is explained in order to perform correct calculations of probabilities for finite sample spaces. 

    SPECIFIC OUTCOME 4 
    Interpret probability contextually and explain the role of probability in life tables. 

    ASSESSMENT CRITERIA     

    ASSESSMENT CRITERION 1 
    The probabilities zero and one of events are interpreted in terms of the context provided. 

    ASSESSMENT CRITERION 2 
    The probability is interpreted contextually in relation to the interpretation of p-values to reflect the logic of statistical inference. 

    ASSESSMENT CRITERION 3 
    The use of probability in constructing life tables is explained to illustrate an important application of probability. 


    UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS 
    The assessment will be governed by the policies and guidelines of the relevant Education and Training Quality Assuror (ETQA) that has jurisdiction over this field of learning.

    The assessor will (at the very least) be accredited and have a relevant qualification and be a subject matter expert in this learning area and at least have 3 years experience in the skills specific area, post qualification.

    The learner can be assessed against this unit standard to obtain credits or as part of an integrated assessment for a qualification.
  • Internal moderation.
  • External moderation.
  • An assessor, accredited by the relevant ETQA, will assess the learner's competency.
  • Assessment procedures will be supplied by the ETQA in alignment with NSB requirements.
  • All assessment activities must be fair, so that all candidates have equal opportunities. Activities must be free of gender, ethnic or other bias.
  • Assessment and moderation procedures, activities and tools must be transparent, affordable and support development within the field, sub-field and NQF.
  • Questions and answers to determine theoretical knowledge are expected.
  • Assessment of a portfolio of evidence.
  • Direct observation in simulated and/or controlled work conditions. 
    		•

    UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE 
    Names, functions and locations of:
  • Venn diagrams.
  • Life tables.

    Purpose of processes and procedures of:
  • Purpose of the investigation.
  • The role of probability in life tables.
  • The role of probability in statistical inference.

    Attributes, properties, characteristics related to:
  • Independent and dependent events.
  • Mutually exclusive events.
  • Union and intersection of events.
  • Conditional events.

    Cause and effect, implications of:
  • Interpretation of probability contextually is related to the interpretation of p-values to reflect the logic of statistical inference.

    Procedures and techniques:
  • Venn diagrams.
  • Calculation of probabilities of events.
  • Use of probability in constructing life tables.

    Regulations, legislation, agreements, policies:
  • National Statistical Offices.
  • National Statistics Act.

    Theory, rules, laws, principles:
  • Concepts of certainty and uncertainty.
  • Concepts of probability.
  • Probability axioms.
  • Probability laws.
  • Bayes' theorem.
  • Conditional probability.

    Relationships, systems:
  • Between probability and statistical inference.
  • Between probability and decision making. 
    		•

    UNIT STANDARD DEVELOPMENTAL OUTCOME 
    N/A 

    UNIT STANDARD LINKAGES 
    N/A 


    Critical Cross-field Outcomes (CCFO): 

    UNIT STANDARD CCFO IDENTIFYING 
    Identifying and solving problems in which responses display that responsible decisions using critical and creative thinking have been made when:
  • Recognising the problem to be solved and utilising probability in decision making. 
    		•

    UNIT STANDARD CCFO WORKING 
    Working effectively with others as a member of a team, group, organisation, and community during:
  • Consultation with supervisor. 
    		•

    UNIT STANDARD CCFO ORGANISING 
    Organising and managing oneself and one's activities responsibly and effectively when:
  • Calculating probabilities to solve a specific problem. 
    		•

    UNIT STANDARD CCFO COLLECTING 
    Collecting, analysing, organising and critically evaluating information to better understand and explain:
  • The concepts of certainty and uncertainty.
  • The concepts of probability. 
    		•

    UNIT STANDARD CCFO COMMUNICATING 
    Communicating effectively using visual, mathematical and/or language skills in the modes of oral and/or written persuasion when:
  • Interpreting probabilities in terms of the context provided.
  • Explaining the role of probability in life tables. 
    		•

    UNIT STANDARD CCFO SCIENCE 
    Using science and technology effectively and critically, showing responsibility towards the environment and health of others when:
  • Using probability in constructing life tables.
  • Using Venn diagrams to explain the laws of probability.
  • Calculating the probability of events using the laws of probability. 
    		•

    UNIT STANDARD CCFO DEMONSTRATING 
    Demonstrating an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation when:
  • Recognising the role of probability in constructing life tables.
  • Recognising the role of probability in statistical decision making on the social, political, economic, legislative and environmental contexts. 
    		•

    UNIT STANDARD ASSESSOR CRITERIA 
    N/A 

    REREGISTRATION HISTORY 
    As per the SAQA Board decision/s at that time, this unit standard was Reregistered in 2012; 2015. 

    UNIT STANDARD NOTES 
    N/A 

    QUALIFICATIONS UTILISING THIS UNIT STANDARD: 
      ID QUALIFICATION TITLE PRE-2009 NQF LEVEL NQF LEVEL STATUS END DATE PRIMARY OR DELEGATED QA FUNCTIONARY
    Core  65649   National Certificate: Official Statistics  Level 5  Level TBA: Pre-2009 was L5  Passed the End Date -
    Status was "Reregistered"     		 2023-06-30  PSETA 


    PROVIDERS CURRENTLY ACCREDITED TO OFFER THIS UNIT STANDARD: 
    This information shows the current accreditations (i.e. those not past their accreditation end dates), and is the most complete record available to SAQA as of today. Some Primary or Delegated Quality Assurance Functionaries have a lag in their recording systems for provider accreditation, in turn leading to a lag in notifying SAQA of all the providers that they have accredited to offer qualifications and unit standards, as well as any extensions to accreditation end dates. The relevant Primary or Delegated Quality Assurance Functionary should be notified if a record appears to be missing from here.
     
    NONE 


    All qualifications and part qualifications registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.