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

• 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]

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

• Construct a frequency distribution by grouping data into classes.

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

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

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

• Construct a histogram.
• Interpret a histogram.

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].