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Classifying Data, SM-Bank 017

Explain the difference between continuous and discrete data, giving an example of each.  (3 marks)

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\(\text{See worked example}\)

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\(\text{Discrete can be assigned a numerical value and can}\)

\(\text{usually be counted.}\)

\(\text{Examples could include:} \)

  • \(\text{The number of people living in a household}\)
  • \(\text{The number of people catching the 4:10 pm train}\)
  • \(\text{The number of cars park at Westfield on Monday}\)

\(\text{Continuous data can be assigned any value in a range}\)

\(\text{and usually involves a measurements.}\)

\(\text{Examples could include:} \)

  • \(\text{The weights of parcels at the post office}\)
  • \(\text{The heights of students in Year 7}\)
  • \(\text{The temperatures recorded at Sydney during March}\)

Classifying Data, SM-Bank 015 MC

Organisers were choosing relay teams for the regional athletics carnival.

They asked the following question.

'What were the times for the 15 Years boys relay teams at zone athletics carnivals?'

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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\(D\)

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\(\text{The times recorded are measurements}\)

\(\text{so all numbers on the scale are possible}\)

\(\longrightarrow\ \text{Numerical, continuous.}\) 

\(\Rightarrow D\)

Classifying Data, SM-Bank 012

Which of the following is an example of numerical continuous data?

  1. The weights of babies born in a hospital during the month of May
  2. The types of cars sold at a car yard
  3. The number of funnel-web spiders collected by the Australian Reptile Park in 2023
  4. The colours used in the American flag
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\(A\)

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\(\text{Weights are measurements (quantitative) }\longrightarrow\ \text{numerical continuous}\)

\(\Rightarrow A\)

Classifying Data, SM-Bank 011 MC

Which of the following is an example of numerical discrete data?

  1. The minimum temperature in each capital city on Monday morning
  2. The number of competitors in a triathlon
  3. The different types of snakes in a reptile display
  4. The lengths of earth worms in a garden
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\(B\)

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\(\text{The number of competitors in a triathlon can be counted }\longrightarrow\ \text{numerical discrete}\)

\(\Rightarrow B\)

Classifying Data, SM-Bank 009

State whether the following data is categorical or numerical.  If numerical, state whether discrete or continuous.

  1. The distance thrown by the 15 years javelin champion.  (1 mark)

  2. The types of fruit used in a fruit salad.  (1 mark)

  3. The number of students travelling to the Year 7 camp by bus.  (1 mark)

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a.    \(\text{Numerical continuous}\)

b.    \(\text{Categorical}\)

c.    \(\text{Numerical discrete}\)

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a.    \(\text{Data is a measurement}\ \longrightarrow\ \text{Numerical continuous}\)

b.    \(\text{Fruit is grouped into categories or types}\ \longrightarrow\ \text{Categorical}\)

c.    \(\text{Students can be counted}\ \longrightarrow\ \text{Numerical discrete}\)

Classifying Data, SM-Bank 008

Match each variable with its classification on the right.  (2 marks)

\begin{array} {ll} \text{A.  Hair colour of students in Year 7} &\text{1.  Numerical discrete} \\\text{B.  Heights of players in the Boomers basketball team} & \text{2.  Categorical ordinal} \\\text{C.  The number of people living in each household in NSW}\  & \text{3.  Numerical continous}\\\text{D.  A, B, C, D, E grades on a report card}  & \text{4.  Categorical nominal}\end{array}

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\(\text{A}\longrightarrow 4,\ \text{B}\longrightarrow 3,\ \text{C}\longrightarrow 1,\ \text{D}\longrightarrow 2\)

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\(\text{A. Hair colour is data grouped in categories with no order}\)

\(\therefore\ \text{4. Categorical nominal}\)

\(\text{B. Heights are measurements which are numerical and continuous}\)

\(\therefore\ \text{3. Numerical continous}\)

\(\text{C. The people living in each household are counted}\)

\(\therefore\ \text{1. Numerical discrete}\)

\(\text{D. Grades on a report card are categorical but the order is important}\)

\(\therefore\ \text{2. Categorical ordinal}\)

Classifying Data, SM-Bank 007

Classify the following as either categorical or numerical data. 

  1. The colours of the cars entering a shopping centre.  (1 mark)

  2. The temperatures recorded in Brisbane over a 2 week period.  (1 mark)

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a.    \(\text{categorical}\)

b.    \(\text{numerical}\)

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a.    \(\text{Colours of cars are words therefore categorical.}\)

b.    \(\text{Temperatures are measurements therefore numerical.}\)

Classifying Data, SM-Bank 004 MC

The variables age (under 55 years, 55 years and over) and preferred travel destination (domestic, international) are

  1. both categorical variables.
  2. both numerical variables.
  3. a numerical variable and a categorical variable respectively.
  4. a categorical variable and a numerical variable respectively.
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\(A\)

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\(\text{Age is a categorical ordinal variable}\)

\(\text{because it is categorical data that can}\)

\(\text{have an order.}\)

\(\text{Preferred travel destination is a categorical}\)

\(\text{nominal value because the data has a name.}\)
 

\(\Rightarrow A\)

Classifying Data, SM-Bank 003

The variables blood pressure (low, normal, high) and age (under 50 years, 50 years or over) are

  1. both nominal variables.
  2. both ordinal variables.
  3. a nominal variable and an ordinal variable respectively.
  4. an ordinal variable and a nominal variable respectively.
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\(B\)

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\(\text{Blood pressure is an ordinal variable}\)

\(\text{because it is categorical data that can}\)

\(\text{have an order.}\)

\(\text{Under 50 and over 50, likewise, is an}\)

\(\text{ordinal variable.}\)
 

\(\Rightarrow B\)

Classifying Data, SM-Bank 002 MC

The variables recovery time after exercise (in minutes) and fitness level (below average, average, above average) are

  1. both numerical.
  2. an ordinal variable and a nominal variable respectively.
  3. a numerical variable and a nominal variable respectively.
  4. a numerical variable and an ordinal variable respectively.
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\(D\)

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\(\text{Recovery time in minutes → numerical variable}\)

\(\text{Fitness level → ordinal (categories that can be ordered)}\)

\(\Rightarrow D\)

Classifying Data, SM-Bank 001 MC

The variables

region (city, urban, rural)

population density (number of people per square kilometre)

  1. are both categorical.
  2. are both numerical. 
  3. are categorical and numerical respectively.
  4. are numerical and categorical respectively.
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\(C\)

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\(\text{Region is a categorical variable and population}\)

\(\text{density is a numerical variable (i.e. it can be}\)

\(\text{represented by countable numbers).}\)

\(\Rightarrow C\)

Statistics, STD2 S1 2018 HSC 3 MC

A survey asked the following question.

'How many brothers do you have?'

How would the responses be classified?

  1. Categorical, ordinal
  2. Categorical, nominal
  3. Numerical, discrete
  4. Numerical, continuous
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`text(C)`

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`text(The number of brothers a person has is)`

`text(an exact whole number.)`

`:.\ text(Classification is numerical, discrete.)`

`=>\ text(C)`