Unit 6: Data Handling
Lecture 1: Representing Data
Learning Objectives
–  To be able to collect data in a tally table.
–  To recognise the difference between discrete and
continuous data.
–  To be able to represent data using a bar chart,
frequency diagram, frequency polygon and
histogram.
Key Words
– 
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– 
– 
– 
– 
Data
Discrete
Continuous
Tally
Bar chart
Frequency diagram
– 
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Frequency polygon
Histogram
Frequency
Qualitative
Quantitative
Data
–  Data is another word for information.
–  One way to collect data is using a survey or a
questionnaire.
–  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
–  Numerical data is quantitative.
•  E.g. cost of a shirt
–  Non-numerical data is qualitative.
•  E.g. the colour of a shirt
Discrete and Continuous
–  Discrete data can be counted. They can take particular
values.
•  e.g. Number of children, number of trees in a garden.
–  Continuous data results when measuring things like
length, time and mass. It cannot be measured exactly.
•  e.g. The time taken to run 100m. It could be 9s or 9.8s or 9.81s. It
can also be measured more accurately.
Discrete or Continuous?
•  Are these examples of discrete or continuous data?
a. 
b. 
c. 
d. 
e. 
f. 
Number of aces served by Roger Federer per match.
The heights of the Chinese basketball team.
The shoe sizes of the British women's hockey team.
The times from the 400m race in the Olympics.
The number of medals won by the British team at the Olympics.
The number of goals scored by Manchester United in each of match
this season.
g.  The speed with which Steven Gerrard kicks the ball to score the
winning goal for Liverpool.
Raw Data
•  Sally carried out a survey of shoe sizes. Her results are
below:
•  4
•  5
•  3
5
3
7
6
7
2
4
4
5
4
5
4
3
6
3
2
6
4
4
4
5
–  This is the raw data. It is not organised in any way.
–  Is it discrete or continuous data?
–  The first thing to do to begin to analyse the data is to organise it
into a tally chart.
Using Tally Marks
Shoe size
2
3
4
5
6
7
Tally
Total
Frequency
2
4
8
5
3
2
24
Each tally mark represents one piece of data. Groups of 5 are
represented as
.
Frequency gives the total count of each size
Drawing a Bar Chart
Frequency
–  The data on shoe sizes is discrete data.
–  Therefore, you can draw a bar chart.
Frequency
9
8
7
6
5
4
3
2
1
0
Bar chart to show shoe sizes
Frequency
21
32
43
54
Shoe size
6
5
76
Grouping Data
•  The marks of 30 students in an exam are marked out of 50.
• 
• 
• 
• 
22
39
35
36
32
18
28
33
29 7 13 41 34 28 27
33 45 28 39 31 17 41
15 8 33 47 21 27 34
29
•  The data is so spread
•  out that it is easier to
•  organise it into groups.
Mark
1-10
11-20
21-30
31-40
41-50
Tally
Frequency
Frequency Table
•  This is a frequency
table. It represents
the data, but without
the tally marks shown.
•  The data can be
represented using a
bar chart.
Mark
Frequency
1-10
2
11-20
4
21-30
9
31-40
11
41-50
4
Continuous Data
•  When grouping continuous data, the groups need to be displayed
using ≤ and < signs.
The lengths of times that a restaurant takes to serve food are
surveyed. The first 8 results are:
15, 11, 17, 12, 21, 28, 19, 15
The tally table would look like this:
Time, t(min)
10≤ t < 15
15≤ t < 20
20≤ t < 25
25≤ t < 30
Tally
Frequency
The first group includes all the
times up to, but not including
15mins. So up to 14.999999….
mins. The next group goes up
to, but not including 20 and so
on.
Representing Continuous Data
•  The table below shows length of time it takes to serve
meals at Jake’s Grill.
Time, t(min)
Frequency
10≤ t < 15
1
15≤ t < 20
7
20≤ t < 25
16
25≤ t < 30
25
30≤ t < 35
19
35≤ t < 40
2
  The data is continuous and can
be represented using a
frequency diagram or a
frequency polygon.
  A frequency diagram has a
numerical scale along the
horizontal axis and there are no
gaps between the bars.
Frequency Diagrams
•  This is a frequency diagram of the data from Jake’s Grill.
30
25
Frequency
20
15
10
5
0
10
15
20
25
Time in minutes
30
35
40
45
Joining the Midpoints
•  Another graph can be created by joining the midpoints of
the bars.
30
25
Frequency
20
15
10
5
0
10
15
20
25
Time in minutes
30
35
40
45
Frequency Polygon
•  Removing the bars, leaves a frequency polygon.
30
25
Frequency
20
15
10
5
0
10
15
20
25
Time in minutes
30
35
40
45
Comparing Data
•  Data on serving times is collected from another
restaurant.
  Sally’s Cafe
Time, t(min)
Frequency
10≤ t < 15
8
15≤ t < 20
21
20≤ t < 25
29
25≤ t < 30
6
30≤ t < 35
4
35≤ t < 40
2
  Frequency polygons can be drawn for Jake’s Grill and Sally’s
café on the same axes to compare the data.
Comparing Frequency Polygons
•  Use the polygon to compare the time taken to serve food at the two
restaurants.
Sally’s Cafe
Jake’s Grill
30
Frequency
25
20
15
10
5
0
10
15
20
25
30
Time in minutes
35
40
45
Histograms
–  A histogram is a type of frequency diagram for
grouped continuous data.
–  Sometimes frequency distributions have groups of
different sizes. A histogram uses frequency density
so that the area of the bar represents the
frequency no matter how wide it is.
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.
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”.
Histogram
Length of call, x,
minutes
Frequency, f
Class width
(minutes)
Frequency
density
0≤ t < 10
5
10
5÷10 = 0.5
10≤ t < 15
15
5
15÷5 = 3
15≤ t < 20
18
5
18÷5 = 3.6
20≤ t < 30
16
10
16÷10 = 1.6
  You can then draw a histogram.
  It is similar to a frequency diagram, only the vertical axis is
frequency density instead of frequency.
Drawing a Histogram
4
Frequency Density
3.5
3
2.5
2
1.5
1
0.5
0
5
10
15
20
25
Length of call (minutes)
30
Recap
–  Describe the difference betweendiscrete and
continuous data.
–  What different ways are there to represent the
data?
Unit 6 Lecture 1
Any questions?