Descriptive Statistics

Summary :

Descriptive statistics organise and summarise data so patterns become clear. This chapter shows how to display data with stem-and-leaf plots, histograms, and box plots, then how to measure the centre of a data set using the mean, median, and mode, and its spread using the range, variance, and standard deviation.

Displaying Data Graphically

Once data is collected it must be organised before it can be understood. Graphs turn a long list of numbers into a shape the eye can read. Stem-and-leaf plots and line graphs keep the original values visible, histograms and frequency polygons show how often values occur across intervals, and box plots summarise the spread and highlight the median and quartiles. Choosing the right display depends on the data and the question being asked.

Measures of the Centre

A single value can represent where a data set is centred. The mean is the arithmetic average, found by adding the values and dividing by how many there are. The median is the middle value once the data is ordered, and it is less affected by extreme values. The mode is the value that occurs most often. When a distribution is skewed, the mean is pulled toward the longer tail, so the median often describes typical values better.

Measures of Spread and Location

Spread describes how far the data is scattered around its centre. The range is the difference between the largest and smallest values, while the variance and its square root, the standard deviation, measure the average distance of values from the mean. Location measures such as quartiles and percentiles mark the points below which a given fraction of the data falls, and together these summarise both the width and the shape of a data set.