Definitions and vocabulary used in statistics
This is data which describes something categorical, e.g. "He is tall", "She has blue eyes".
Favourite types of music:
These categories describe types of music, not quantities, so they are qualitative data.
This is data which can be counted in numbers. It can be either continuous or discrete.
Heights of students in a class (in centimetres):
These values are numerical and measurable, so they are quantitative data.
This is data which can be measured.
Temperatures recorded throughout a day (in °C):
Temperature can take any value within a range and can be measured more precisely (e.g., to 1 decimal place, 2 decimal places, etc.), so it is continuous data.
This is data which can be counted, e.g. number of legs, number of sunny days in June.
Discrete data is restricted to certain values, often whole numbers.
Discrete data can be ordinal or nominal.
Number of goals scored in football matches:
You cannot score 2.5 goals — only whole numbers are possible — so this is discrete data.
(Ordered category data)
This is data which has categories which can be counted and ordered.
Customer satisfaction ratings:
These categories have a meaningful order, but the “distance” between them is not measurable.
(Unordered category data)
This is data which can be counted but not ordered.
Types of pets owned:
These categories have no meaningful order — they are just labels — so this is nominal data.
The data is often displayed by a bar chart, pie chart or pictograph.
This is because a numerical relationship cannot be deduced for the information between the categories.
A population is the complete set of persons, values or things for which data is being collected.
For example, all dogs in the UK would form the target population for a statistical analysis on dog food preferences.
Suppose a vet wants to study the average weight of dogs in a town.
The population is:
If the vet only weighs a smaller group of dogs, that smaller group becomes the sample, used to estimate the average weight of the whole population.
A census collects data from the whole population.
Suppose a town wants to know how many dogs live there.
A census would involve:
This gives perfect information, but it takes far more time and effort than studying a smaller sample.
A sample collects data from a part of the population.
Suppose the population is all dogs living in a town.
A sample might be:
These 50 dogs represent the whole population, allowing a vet or researcher to estimate things like the average weight or common health conditions without examining every single dog.
The batch size is the number of bits of data in the sample. It is given the letter n.
Example
n = 15
The smallest data value in a batch is called the lower extreme and is given the symbol EL.
The largest data value in a batch is called the upper extreme and is given the symbol EU.
For the maths test scores data above, EL = 34% and EU = 86%.
Quartiles cut the data into quarters.
Q1 (also known as QL) is the lower quartile. This is the median of the lower half of data.
Q3 (also known as QU) is the upper quartile. This is the median of the upper half of data.
Each quartile represents 25%, so 50% of the data is represented between Q1 and Q3.
There are three commonly used averages: mean, median and mode,
Consider the data set:
4, 7, 7, 9, 10
Each average tells us something slightly different about the data.
These are sometimes called measures of location.
Charts are used to display data visually.
These charts are commonly used in school statistics and everyday data presentation.
