Descriptive Statistics

descriptive statistics

simple methods to summarise data to plot various graphs and find various summary statistics

statistics

collecting, analysing, interpreting data in the best possible way

qualitative data collection

non-numerical data that can be classified into nominal or ordinal data

population

the universe of objects/people of interest

sample

a subset of the population

→ must be representative of the population from which it is drawn

random sample

each element in the population has an equal chance of being drawn

qualitative data

variables which can be measured in numerical terms

quantitative data

non-numerical data that can only be classified into 1 group of categories

discrete variable

variable that takes only a finite number of values or an infinite number of integer valuesco

continuous variable

can take any value in a particular interval

raw data

unprocessed observations

grouped data

observations that are ordered into groups or classes

summarising data

pick out the most important features of a set of data to be able to understand and interpret them

methods of summarising data

• frequency tables

• cumulative frequency distribution

frequency tables - DISCRETE DATA

• summary table showing all possible categories with their frequencies

• uses grouped data

need to work out:

• frequency

• relative frequency of each class

• percent frequency of each class

relative frequency of a class

percent frequency of a class

frequency distribution - CONTINUOUS DATA

• most economic data is continuous and non-integer

steps:

• determine the number of non-overlapping classes

• determine the size of each class

• determine the class limits

• count the number of observations in each interval

approximate class size

class limit

• each data value belongs to 1 class only

• halway between the lower and upper class limits = midpoint/classmark

cumulative frequency distribution

• shows the number of items less than or equal to the UPPER class limit of each class

steps:

• frequency

• cumulative frequency

• percent frequency

• cumulative percent frequency

types of graphical presentation

• pie chart

• bar chart

• histogram

• frequency polygon

• ogive

pie chart

• represents relative frequency of observations by the section of a circle

• area of each section is proportional to the number of observations in the category

• useful for when you have 4-8 categories

bar chart

• presents discrete (qualitative) data

• height of each bar is proportional to the number of observations

• vertical axis = frequency, relative frequency, % frequency scale

histogram

• constructed from a frequency table

• presentation of a frequency distribution and relative frequency distribution of CONTINUOUS data

steps histogram

• horizontal axis = class intervals

• vertical axis = % frequencies

• draw rectangles with centres at the class marks, areas proportional to class frequencies

frequency curve (polygon)

• use the histogram and connect the midpoints at the top of each box together

ogive (cumulative frequency curve)

• graph of cumulative distribution

• horizontal axis = upper class limits

• vertical axis = cumulative % frequency scale

• shows that eg 32% of observations are less than £200

format

• plot points corresponding to cumulative frequency of each class at the upper class limit

• join the points by a straight line to complete the ogive