
12.1 
Data Collection, Organisation and Representation Process, and Interpretation of Data Representation 


Generate statistical questions and collect relevant data: 

1. Statistical question 

Definition 
A question that can be answered by collecting data and there will be variability or diversity in the data related to the question.



2. Data collection method 

Method 
Example 
Interview 
To find out how the students travel to school. 
Survey 
To find out the favourite television programmes of the students. 
Observation 
To count how many cars pass through the junction every hour. 
Experiment 
To record the temperature of hot water as it cools down every five minutes. 


Classify data and construct frequency tables: 

3. Classifying the data 

Categorical data
 Measures characteristic.
 Cannot be measured numerically but can be described.
 Examples: The gender of a person, colours of cars, flavours of sweets, blood groups


Numerical data
 Measures quantity.
 Measured numerically.
 Examples: The number of books read in a week, the height of the badminton players, the time spent on exercise


Discrete data 
Continuous data 
Measured in a whole unit 
Measured on a continuous scale 
Example: The number of family members is \(6\) people. 
Example: The mass of the students are \(53\text{ kg}\), \(56.2\text{ kg}\) and \(66.5\text{ kg}\). 


4. Constructing a frequency table 

 Ungrouped data is an unprocessed raw data.


Example 
The data shows the number of children in each family for \(20\) families.
\(2\quad0\quad1\quad1\quad2\quad1\quad3\quad0\quad4\quad3 \\2\quad4\quad1\quad0\quad2\quad1\quad0\quad2\quad2\quad3\\\)

Number of children 
Tally 
Frequency 
\(0\) 
\(\) 
\(4\) 
\(1\) 
\(\cancel{}\) 
\(5\) 
\(2\) 
\(\cancel{}\space\) 
\(6\) 
\(3\) 
\(\) 
\(3\) 
\(4\) 
\(\) 
\(2\) 
Total 
\(20\) 



Construct data representations: 

(i) Bar chart 

 A type of data representation which represents data by using bars.
 Suitable for showing comparisons between categories.
 The bars in a bar chart can be drawn horizontally or vertically.


Steps to construct a bar chart.
 Draw the horizontal and vertical axes on a grid.
 Choose one of the axes to mark a suitable scale and label the axis.
 Label the other axis.
 Draw the bars such that the height of each bar corresponds to the frequency of the category it represents.
 Write down the title of the bar chart.


Examples 
(i) Vertical bar chart

(ii) Horizontal bar chart

(iii) Dual bar chart
 A dual bar chart is suitable for comparing two sets of data.



When representing data using a bar chart:
 the width of each bar must be uniform.
 the bars need to be evenly spaced.


(ii) Pie chart 

 A data representation that uses sectors of a circle to show the portion of each category of the whole data.


Steps to construct a pie chart.
 Find the angle of sector for each category.
 Draw a circle and divide it into different sectors based on the angles calculated.
 Label each sector.
 Write down the title of the pie chart.


Example 



(iii) Line graph 

 A data representation used to display changes of data over a period of time.
 The data is represented by points which are connected in a straight line.
 The horizontal axis usually represents the time duration and the vertical axis usually represents the frequency values.


Steps to construct a line graph.
 Draw the horizontal and vertical axes on a grid.
 Choose a suitable and uniform scale for both axes. The vertical axis represents data. The horizontal axis represents time.
 Plot the points and connect the points in a straight line.
 Write down the title of the line graph.


Example 



(iv) Dot plot 

 Shows the distribution of data on a number line.
 The data are either clustered around certain values or spread out evenly on a number line.
 Can help us to visualise data patterns, draw inferences and make decisions.
 Can also detect unusual observations (extreme values).


Steps to construct a dot plot.
 Draw a horizontal number line that covers the range of the given data.
 Plot the individual data with a dot over their values on the number line.
 Write down the title of the dot plot.


Example 



(v) Stemandleaf plot 

 A data representation that separates the data values into stem and leaf according to their place value.
 The leaf usually is the last digit of the number.
 The stem is the remaining digit or digits on the left of the number.


Steps to construct a stemandleaf plot.
 Write each data one by one and take the tens digit of each data value as the stem.
 The last digit of the number is written on the leaf.
 Rearrange the leaves in ascending order.
 Write a key and the title. The key indicates the unit for the stem and leaf.


Example 



Convert a data representation to another representation: 

 A data representation can be converted to other suitable representations for further analysis.


Interpret data representations: 

 Can obtain information and hence make inferences and predictions.


(i) Histogram 

 A data representation that displays grouped data.
 Grouped data is data that is collected in intervals.
 The width of each bar in a histogram represents a specific interval.
 The height of each bar represents the frequency in each interval.


Example 



 A histogram does not display the actual values of the data but displays values in a certain interval.
 A histogram can provide a display of large data sets because the data is represented in class intervals.


(ii) Frequency polygon 

 A graph formed by joining the midpoint of the top of each bar in a histogram with straight lines.


Example 



The importance of representing data ethically: 

 Help us to analyse and interpret data much easier.
 To avoid confusion.


To represent the data ethically,
 the scale used in the representation must be consistent and start at \(0\).
 the data displayed must be accurate.

