Random Variables

Numerical since measures the quantity or number of something, and hence arithmetic processes such as adding and subtracting, or calculating an average, make sense.

Categorical since the possible responses may be one of a set of groupings or classifications.

Numerical as counting will provide responses which are numbers quantifying the amount of something.

First we decide that it is categorical, since the possible responses fall into a category such as Soccer, Karate, Netball, etc, it is not quantifying an amount of something.

First we decide that it is numerical, since rainfall is a quantity or numerical amount.

Categoricalsince the possible responses fall into a category such as Brown, Blue, Green, etc.

Numericalsince the since temperature is a quantity or numerical amount.

Numericalsince number of power failures is a quantity or numerical amount, counting the number of times something occurs.

Categorical, since the possible responses fall into a category or group.

Numerical as a count.

Numerical as age is a quantity or numerical amount quantify a duration of time.

Categorical as responses are grouped according to upholstery type.

Numerical as measured in m/s.

Numerical as measured in Megawatts/hour.

Categorical, since response is one of a number of groups. NOTE: Despite the labels for each group being numbers, they don’t represent a particular numerical quantity, they are merely labels for the ordered categorical responses).

First we decide that it is categorical, since the possible responses fall into a category such as Soccer, Karate, Netball, etc, it is not quantifying an amount of something.
Then we decide whether it is nominal or ordinal.
Nominal since there is no natural order to the possible responses (apart from alphabetical arrangement).

First we decide that it is numerical, since rainfall is a quantity or numerical amount.
Then we decide whether it is nominal or ordinal.
Continuous since rainfall in millimetres can assume any value along a continuum or range (i.e., it can be measured as precisely as the measuring instrument allows, e.g., it could be measured to many decimal places). It doesn’t only assume one of a set of distinct possible values. Don’t be tricked by a measurement being ‘in millimetres’…we could still say it was 45.7 millimetres or 45.7693 millimetres etc, depending on precision of measuring instrument.

Categoricalsince the possible responses fall into a category such as Brown, Blue, Green, etc.
Nominal since there is no natural order to the possible responses (apart from alphabetical arrangement).

Numericalsince the since temperature is a quantity or numerical amount.
Continuous since temperature can assume any value along a continuum or range (i.e., it can be measured as precisely as the measuring instrument allows, e.g., it could be measured to many decimal places). It doesn’t only assume one of a set of distinct possible values.

Numericalsince number of power failures is a quantity or numerical amount, counting the number of times something occurs.
Discrete since it is counting the number of occurrences, there cannot be 1.76 power failures for example.

Categorical, since the possible responses fall into a category or group.
Ordinal since there IS a natural order to the possible responses (‘under 18 years’ is lower along the age scale than ’18 to less than 35 years’, and so on.

Numerical as a count.
Discrete as a count can only take whole values in a range.

Numerical as age is a quantity or numerical amount quantify a duration of time.
Continuous since age can assume any value along a continuum or range (i.e., it can be measured as precisely as the measuring instrument allows, e.g., it could be measured to many decimal places). It doesn’t only assume one of a set of distinct possible values. Don’t be tricked by a measurement being ‘in years’…we could still identify someone was 18.5 years, or 18.52 years, etc.

Categorical as responses are grouped according to upholstery type.
Nominal as the categories have no natural order

Numerical as measured in m/s.
Continuous as flow rate is a measurement which can take any value in a range

Numerical as measured in Megawatts/hour.
Continuous as electricity produced is a measurement which can take any value in a range.

Categorical, since response is one of a number of groups. NOTE: Despite the labels for each group being numbers, they don’t represent a particular numerical quantity, they are merely labels for the ordered categorical responses).
Ordinal since the list of possible categories have a natural order from ‘none’ though to ‘full’.