# 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 ($\scriptsize \bar{x}$), median ($\scriptsize {{M}_{e}}$) and modal ($\scriptsize {{M}_{o}}$) values of grouped data using the formulae:
• $\scriptsize \bar{x}=\displaystyle \frac{{\sum {{f}_{i}}{{x}_{i}}}}{n}$
• $\scriptsize {{M}_{e}}=l+\displaystyle \frac{{\left( {\displaystyle \frac{n}{2}-F} \right)}}{f}\times C$
• $\scriptsize {{M}_{o}}=l+\displaystyle \frac{{{{f}_{m}}-{{f}_{{m-1}}}}}{{2{{f}_{m}}-{{f}_{{m-1}}}-{{f}_{{m+1}}}}}\times c$

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