# 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].