Data handling: Calculate, represent and interpret measures of central tendency and dispersion in univariate numerical grouped data

Subject outcome

Subject outcome 4.2: Calculate, represent and interpret measures of central tendency and dispersion in univariate numerical grouped data.

Learning outcomes

  • Construct a frequency distribution table by grouping data into classes.
  • Calculate the cumulative frequency and plot the ogive curve.
  • Use the ogive curve to estimate quartile values.
  • Construct histograms using tabulated grouped data.
  • Calculate the mean ([latex]\scriptsize \bar{x}[/latex]), median ([latex]\scriptsize {{M}_{e}}[/latex]) and modal ([latex]\scriptsize {{M}_{o}}[/latex]) values of grouped data using the formulae:
    • [latex]\scriptsize \bar{x}=\displaystyle \frac{{\sum {{f}_{i}}{{x}_{i}}}}{n}[/latex]
    • [latex]\scriptsize {{M}_{e}}=l+\displaystyle \frac{{\left( {\displaystyle \frac{n}{2}-F} \right)}}{f}\times C[/latex]
    • [latex]\scriptsize {{M}_{o}}=l+\displaystyle \frac{{{{f}_{m}}-{{f}_{{m-1}}}}}{{2{{f}_{m}}-{{f}_{{m-1}}}-{{f}_{{m+1}}}}}\times c[/latex]

Unit 1 outcomes

By the end of this unit you will be able to:

  • Construct a frequency distribution by grouping data into classes.

Unit 2 outcomes

By the end of this unit you will be able to:

  • Work out class intervals.
  • Plot the ogive.
  • Interpret the ogive.

Unit 3 outcomes

By the end of this unit you will be able to:

  • Construct a histogram.
  • Interpret a histogram.

Unit 4 outcomes

By the end of this unit you will be able to:

  • Calculate the mean of grouped data using the formula [latex]\scriptsize \bar{x}=\displaystyle \frac{{\sum {{f}_{i}}{{x}_{i}}}}{n}[/latex].
  • Calculate the median of grouped data using the formula [latex]\scriptsize \displaystyle {{\text{M}}_{e}}=l+\displaystyle \frac{{\left( {\displaystyle \frac{n}{2}-F} \right)}}{f}\times c[/latex].
  • Calculate the modal value of grouped data using the formula [latex]\scriptsize {{M}_{o}}=l+\displaystyle \frac{{{{f}_{m}}-{{f}_{{m-1}}}}}{{2{{f}_{m}}-{{f}_{{m-1}}}-{{f}_{{m+1}}}}}\times c[/latex].

License

Icon for the Creative Commons Attribution 4.0 International License

National Curriculum (Vocational) Mathematics Level 3 by Department of Higher Education and Training is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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