Use data and Probability to solve Problems Online Short Course

Credits 5

COURSE OBJECTIVE

This Unit Standard is designed to provide credits towards the mathematical literacy requirement of the NQF at Level 3. The essential purposes of the mathematical literacy requirement are that, as the learner progresses with confidence through the levels, the learner will grow in:

• a confident, insightful use of mathematics in the management of the needs of everyday living to become a self-managing person
• An understanding of mathematical applications that provides insight into the learner`s present and future occupational experiences and so develop into a contributing worker
• The ability to voice a critical sensitivity to the role of mathematics in a democratic society and so become a participating citizen
• People credited with this Unit Standard are able to:
• Pose questions, collect and organise data.
• Represent and interpret data using various techniques to investigate real life and work problems.
• Use random events to explore and apply probability concepts in simple life and work related situations.

WHAT YOU WILL LEARN:

• Pose questions, collect and organise data.
• Determining trends in societal issues such as crime and health.
• Identifying relevant characteristics of target groups such as age, range, gender, socio-economic group, cultural belief and performance.
• Predicting the likelihood of the occurrence of events.
• Considering the attitudes or opinions of people on issues.
• The selection of a sample from a population with due sensitivity to issues relating to bias.
• The formulation and use of questionnaires and interviews to obtain data for specific purposes related to surveys and censuses.
• Use of databases to obtain information (e. g., StatsSA for national census data) and data suited to the resolution of particular issues.
• Work with deferent types of measuring instruments and scales such as yes/no (dichotomous) 5 point (Likert), discrete, and continuous variables (e g., temperature).
• Evaluation of data gathering techniques and of data collected so that faults and inconsistencies are identified. (e.g., in cases where a person may be counted more than once such as when collecting ST13 data).
• Situations or issues that can be dealt with through statistical methods are identified correctly.
• Variables contributing to a problem situation are identified and addressed in data gathering, e.g. crime is related to time of day and location.
• Appropriate and efficient methods are used to collect, record and organise data.
• Data samples are of adequate size and are representative of the population.
• Represent, analyse and interpret data using various techniques.
• Represent, analyse and interpret data using various techniques to investigate real-life and work problems
• Calculation of measures of centre and spread such as mean, median, mode, range and inter-quartile range.
• Use of scatter plots and intuitively placed lines of best fit to represent the association between two variables. (Regression analysis not included,).
• Fit curves (e g., linear and quadratic cases) to predict trends.
• Use of a variety of representations applicable to the issue being investigated.
• Determining trends societal issues such as crime and health;
• Identifying relevant characteristics of target groups such as age, range, gender, socio-economic group, cultural belief and performance;
• Considering the attitudes or opinions of people on issues.
• Graphical representations and numerical summaries are consistent with the data, are clear and appropriate to the situation and target audience.
• Different representations of aspects of the data are compared to take a position on the issue.
• Calculations and the use of statistics are correct and appropriate to the problem.
• Interpretations of statistics are justified and applied to answer questions about the problem.
• New questions that arise from the modelling of the data are discussed.
• Use random events to explore and apply, probability concepts in simple life.
• Use random events to explore and apply, probability concepts in simple life and work related situations
[Note: straightforward applications relevant to the life or work related experiences of the learners should be chosen]
• Distinguish outcomes, which are equally likely (e.g. spinning a coin, rolling a die) from those that are not (e.g. dropping a drawing pin, spinning a biased coin).
• Distinguish between a trial (e.g. a turn at rolling a die), outcome (getting a 6 when the die is rolled) and event (getting any even number when rolling a die -a collection of outcomes).
• Interpret probability values expressed as fractions between 0 and 1 or as percentages.
• Use the term “odds on” in relation to a probability value (e.g. the odds on getting a 4 when rolling a die are 1 to 5 while the probability of getting a 4 is one sixth).
• Distinguish between theoretical (e. g., for a fair coin on the basis of equal likelihood) and experimental probabilities (e.g. for getting a pin to land with its point up or its point down when dropped on the basis of relative frequency after a large number of trials).
• Use tree diagrams in representing and working with events.
• Use basic counting techniques to determine the number of ways an event can occur. (The formal use of permutations and combinations not expected.)
• Distinguish between situations in which probabilities need to be multiplied from those in which probabilities need to be added (e. g., drawing the ace of hearts and the ace of spades as opposed to drawing one or the other).
• Make and test predictions about probability in the context of games, real-life situations and the workplace.
• Data are gathered, organised, sorted and classified in a suitable manner for further processing and analysis.
• Experiments and simulations are chosen appropriately in terms of the situation to be investigated.
• Probabilities are determined correctly.
• Distinctions are correctly made between theoretical and experimental probabilities.
• Predictions are based on validated experimental or theoretical probabilities.
• The outcomes of experiments and simulations are communicated clearly.

Course delivery and Requirements

This course can be started at any time and is self paced and completely online , You will need an Internet connection and a PC or Laptop to complete this course