REPRESENTATION OF STATISTICAL DATA

Learning Objectives:

- To be able to collect data in tally table
- To recognise the difference between discrete and continous data
- To be able to represent data using a bar chart, frequency diagram, frequency polygon and histogram


Key Words

• Data - Frequency polygon
• Discrete - Histogram
• Continous - Frequency
• Tally - Qualitative
• Bar Chart - Quantitative
• Frequency Diagram 

Data is another word for information. When data is collected there are lots of ways to represent it using different charts, tables and statistics.

There are different types of data:

Quantitative and Qualitative

Quantitative is Numerical data (e.g cost of shirt)

Qualitative is Non-numerical data (e.g the colour of a shirt)

Discrete and Continous 

Discrete data can be counted. They can take particular values (e.g number of children)

Continuous data results when measuring things like length, time and mass. (e.g the time taken to run is 100m)

1) Raw Data, it is not organised in any way,

3 4 5 4 2 4 6 

6 4 1 2 3 4 5

8 7 8 1 3 4 4

5 6 6 5 4 2 5

To begin to analyse the data is to organise it into a 2) Tally chart

Each tally mark represents one piece of data

Frequency gives the total count of each size

Drawing a 3) Bar chart

The data on shoe sizes is discrete data. Therefore, you can draw a bar chart.

Frequency Diagram 

Another graph can be created by joining the midpoints

DRAWING HISTOGRAMS

Each group or class is represented by a bar. There are no gaps between the bars. 

The area of each bar is proportional to the frequency of the class it represents.

FORMULA:

Frequency density = frequency

                                 class width

The frequency density is calculated for each class and gives the height of each bar. 

The vertical axis of the histogram is labelled "frequency density"

It is similar to a frequency diagram, only the vertical axis is frequency density instead of frequency