Types of Data (Edexcel GCSE Statistics)

Types of Collected Data

What types of data do I need to be familiar with?

• There are a number of terms for types of data that you need to be familiar with

  • You need to recognise and understand them when they appear in exam questions

  • And be able to use them when writing your answers to questions

• Raw data is data in exactly the form that it was collected

  • i.e. before it has been organised or processed in any way

• Raw data can be either quantitative or qualitative

  • Quantitative data can be recorded as a number

    • e.g. heights, lengths of time, numbers of people or objects, shoe sizes, etc.

  • Qualitative data cannot be recorded as a number

    • e.g. colours, flavours, kinds of animal, makes of car, etc.

• Quantitative data can be either continuous or discrete

  • Continuous data can take any numerical value on a scale

    • e.g. height, length, weight, mass

    • For continuous data the measurements can become more and more accurate the more you 'zoom in'

  • Discrete data can only take on particular numerical values on a scale

    • Often these are integers (e.g. numbers of people or objects)

    • But they don't have to be integers (e.g. shoe sizes, which include 'half sizes')

• Categorical data is data that can be organised into non-overlapping categories

  • 'Non-overlapping' is important here

    • Each piece of data can belong to one and only one category

    • e.g. heights less than 1.7 metres () and heights greater than or equal to 1.7 metres ()

    • but not and (because a height of 1.7 metres would belong to both categories)

  • The categories can be numerical or non-numerical

• Ordinal data is data that can be written in order

  • If the data is numbers, these can be ordered in the usual way

  • If the data is not numbers, then it must be possible to apply a numerical 'rating scale'

    • e.g. a scale of 1 to 5 with 1 as 'disagree strongly' and 5 as 'agree strongly'

• Bivariate data is data that is collected as pairs of values

  • This could be data collected to investigate

    • the relationship between two variables

    • how changes in one variable affect the other variable

  • e.g. age of car and cost of annual maintenance, train ticket price and length of journey, etc.

• Multivariate data is data that is collected in sets of more than two values

  • e.g. cholesterol levels, blood pressure and weight for a number of patients in a study

What is the difference between primary data and secondary data?

• For the exam, you need to know the difference between primary data and secondary data

  • This includes recognising the advantages and disadvantages of each

• Primary data is data that is collected either by the person who is going to use it, or specifically for the person who is going to use it

  • Advantages of primary data:

    • Can be gathered specifically for the question you are trying to answer

    • The level of accuracy will be known

    • The collection method will be known

  • Disadvantages of primary data:

    • Collecting data can require a lot of time

    • It can also be expensive

• Secondary data is data that has been collected by somebody else

  • Some possible sources for secondary data:

    • the internet

    • print media (newspapers, magazines, etc.)

    • databases

    • research articles

    • census returns

  • Advantages of secondary data

    • Can be quicker to obtain (i.e. less time)

    • Can be easier to obtain (i.e. more convenient)

    • Less expensive than collecting data yourself

    • May be more accurate than data you collect yourself (depending on the source)

  • Disadvantages of secondary data

    • May be hard to find relevant data for your specific question

    • The data may be out of date

    • The level of accuracy may not be known (e.g. the data may have been rounded)

    • The collection method may not be known

    • The source of the data may not be reliable

  • If you use secondary data, it is always necessary to acknowledge the source that the data was taken from

Grouped & Ungrouped Data

What are the advantages and disadvantages of grouping data?

• For a relatively small data set it is okay to leave the data in ungrouped form

  • e.g. the heights (in metres) of eight students in a school club
    
    1.57      1.63      1.69      1.71      1.77      1.79      1.81      1.84

  • There are not too many values in that data set

    • so it is possible to get a 'feel' for the set just by looking at the list of values

• For a large data set it is often more useful to present the data in grouped form

  • The data is divided into a number of categories

    • and the frequency of each category (i.e., the number of values in each category) is reported

  • The categories are known as classes

  • The intervals defining what goes into what class are known as class intervals

• Advantages of using grouped data:

  • The distribution of the data can be seen more clearly

  • Patterns in the data can be spotted more easily

• Disadvantages of using grouped data:

  • The exact data values are no longer visible

    • You can only see how many values fall within each class

  • Statistics calculated from grouped data are less precise

    • e.g. mean, median and mode from grouped data can only be estimates

What things are important when grouping data?

• You must be careful when selecting the class intervals for grouped data

• The class intervals must not overlap

  • For discrete data make sure no data value occurs in more than one class interval

    • e.g. 0-10, 11-20, 21-30, etc.

  • For continuous data the class intervals also must not have any gaps between them

    • e.g. , etc.

    • and would not be good because there is a gap between 10 and 11

• Open-ended class intervals can be used where minimum or maximum values aren't known

  • e.g. for the first class interval

  • or for the last one

• Consider how many class intervals to use for grouping the data

  • If there are too many intervals (too much detail)

  • or too few intervals (not enough detail)

    • then it can be hard to spot trends in the data

• Class intervals do not all need to be the same width

  • You will often see grouped data where the class intervals have equal widths

    • This is appropriate when the data is roughly evenly spread out

  • But sometimes unequal class widths might be more appropriate

    • e.g. when most of the data values are clustered 'in the middle'

    • It might make more sense to have wider intervals at the start and end

    • and narrower intervals in the middle

  • Too many or too few data values falling into certain class intervals

    • can make the data representation less useful

• Also be careful with class intervals when working with rounded data values

  • All values that might round to a particular value must fall within the same class interval

  • e.g. if the data is time rounded to the nearest second

    • then and would not be good intervals to use

    • (because a measurement of 70 seconds to the nearest second could be anywhere between 69.5 and 70.5 seconds)

    • Use and instead

Explanatory & Response Variables

What are explanatory and response variables?

• When data is collected from an experiment, the researcher usually wants to know how changes in one variable affect another variable

  • The first variable is called the explanatory variable (or independent variable)

    • This is the variable that the researcher controls (or observes) changes in

    • The researcher suspects that changes in this variable will cause changes in the other variable

    • The explanatory variable is thought to 'explain' why the other variable changes

  • The second variable is called the response variable (or dependent variable)

    • This is the variable that the researcher measures after changes have been made in the explanatory variable

    • The researcher suspects that this variable will be affected by changes in the explanatory variable

    • The response variable 'responds' to changes in the explanatory variable

  • For example, a researcher wants to study the effects of different types of running shoe on how long it takes runners to run 100 metres

    • The explanatory variable is the type of running shoe

    • The response variable is the time taken to run 100 m

  • Any other variables in an experiment are known as extraneous variables

    • These should be eliminated or minimised so they don't affect the results

• You need to be very careful with explanatory and response variables when drawing a scatter diagram

  • The explanatory variable MUST be on the x-axis

  • And the response variable MUST be on the y-axis