Data Handling
Pupil Notes and worked examples
Key Skill 1: Complete a frequency table
A frequency table shows how obtain data values appear in a dataset.
Example
The pupils in Mr Killean’s class take a Maths test and get scores out of 10, which are listed below:
3
7
6
2
5
9
10
8
7
1
8
4
3
5
6
7
8
7
6
5
3
6
9
8
7
5
9
6
7
8
The pupils were asked to display this information in a frequency table.
The frequency table is below.
There are 5 pupils who
scored 6 out of 10
Key Skill 1: Complete a frequency table (continued)
Grouped Frequency Tables
When data values are widely spread we can group together some of the values to create a
grouped frequency table.
Example
The number of calls from motorists per day for roadside service was recorded for the month of
December 2011. The results were as follows:
28
122
217
130
120
86
80
90
120
140
81
70
40
145
187
113
90
68
174
194
170
120
100
75
104
97
75
123
100
82
109
The grouped frequency table for this set of data values is below.
There were 12 days
where between
80 and 119 motorists
called for roadside
service.
Key Skill 2: Draw a bar chart
In a bar chart, the height of the bar shows the frequency of the result.
As the height of the bar represents frequency, label the vertical axis 'Frequency'.
The labelling of the horizontal axis depends on what is being represented by the bar chart.
9
8
Frequency
7
6
5
4
3
2
1
0
Example
Taking the set of data from Mr Killean’s class from earlier we are going to complete a bar chart.
3
7
6
2
5
9
10
8
7
1
8
4
3
5
6
7
8
7
6
5
3
6
9
8
7
5
9
6
7
8
There are three 9’s
so the bar that
represents the
score of 9 has to
go up to a
frequency of 3
The horizontal axis is labelled ‘Score’ as our data values are scores.
Each bar needs to go as high as its frequency.
There should be an equal space between each bar.
9
8
7
Frequency
6
5
4
3
2
1
0
1
2
3
4
5
6
Score
7
8
9
10
Key Skill 3: Draw a line graph
A line graph is created by plotting a set of points onto a pair of axis and connecting the points
with lines.
The line graph can be used to find and describe trends when comparing two data sets.
Example
Sarah bought a new car in 2001 for $24,000.
The dollar value of her car changed each year as shown in the table below.
Value of Sarah’s Car
Year
Value
2001
$24,000
2002
$22,500
2003
$19,700
2004
$17,500
2005
$14,500
2006
$10,000
2007
$5,800
The data from the table above has been summarised in the line graph below.
You can see from the line graph that the value of Sarah’s car decreases as time progresses.
Key Skill 4: Create a stem and leaf diagram
A stem and leaf diagram is another useful way of displaying information in order.
When a data set is in order you can find the median (the middle value) which represents an
average value for the data set. (see Key Skill 6: Calculate the mean, median and mode of a
given dataset)
You should produce an unordered stem and leaf diagram before ordering your data.
Example
Mr Killean’s class sat an assessment at the end of the school year.
Their scores, out of 50, are below:
7, 36, 41, 39, 27, 21, 25, 17, 24, 31, 17, 13, 31, 19, 6
8, 10, 14, 45, 49, 50, 45, 32, 25, 17, 46, 36, 23, 18, 12
Illustrate these in an ordered stem and leaf diagram.
Unordered
Ordered
0 7 6 8
0 6 7 8
1 7 7 3 9 0 4 7 8 2
1 0 2 3 4 7 7 7 8 9
2 7 1 5 4 5 3
2 1 3 4 5 5 7
3 6 9 1 1 2 6
3 1 1 2 6 6 9
4 1 5 9 5 6
4 1 5 5 6 9
5 0
5 0
n = 30
5 0 means 50
n = 30
5 0 means 50
This is the sample size. It shows how many values are in the data set.
This is the stem and leaf diagrams key.
It shows that the stems are tens and the leaves are units.
All stem and leaf diagrams must have a key and the sample size stated.
Finding the median
0 6 7 8
There are 30 values.
1 0 2 3 4 7 7 7 8 9
This splits the dataset into 2 groups of 15.
2 1 3 4 5 5 7
In this case, to calculate the median find the value in
3 1 1 2 6 6 9
between the 15th and 16th terms.
4 1 5 5 6 9
In between 24 and 25 is 24.5
5 0
Therefore, the average score in the class is 24.5
Key Skill 5: Draw a pie chart
A pie chart is a circle, divided into sections called sectors.
The size of the sectors represents the proportion of each value in a given dataset.
Example
During a recent survey people were asked how many people lived in their household.
Draw a pie chart that represents the data in the table below.
number of
people
1
2
3
4
5 or more
Total
frequency
angle
17
27
15
7
6
72
To complete the angle column use a calculator to find the fraction of the 360° that represents
each sector.
number of
people
frequency
1
17
2
27
3
15
4
7
5 or more
6
Total
72
angle
17
 360  85 °
72
27
 360  135 °
72
15
 360  75 °
72
7
 360  35 °
72
6
 360  30 °
72
360°
27 out of the 72
surveyed have
2 people in their
household
27 ÷ 72 x 360 = 135°
Check that the
total is 360°
Key Skill 5: Draw a pie chart (continued)
Measure 85° to represent the 1 person sector.
Measure 135° to represent the 2 person sector.
Measure 75° to represent the 3 person sector.
Measure 35° sector to leave the 30° sector.
5 or
more
people
4 people
person
1 person
30°
35°
85°
3 people
person
75° 135°
2 people
person
Remember to label all of the sectors.
Key Skill 6: Calculate the mean, median and mode of a given dataset
There are 3 types of average – the mean, the median and the mode.
These provide an indication of the ‘typical’ value of a data set.
_
The mean ( x )
Add up all the values in the data set, then divide by the number of values within the data set.
e.g. Find the mean of the dataset 35, 35, 50, 70, 75
35  35  50  70  75
5
_
265
x
5
_
x
_
x  53
The mean is 53
The median
The middle value of an ordered list. You may have to rewrite the list to order it.
When there is an odd number of values in the dataset find the middle value.
e.g. Find the median of the dataset 35, 35, 50, 70, 75
(35, 35) 50 (70, 75)
The median is 50
When there is an even number of values in the dataset find the mean of the middle 2 values.
e.g. Find the median of the dataset 35, 35, 50, 55, 70, 75
(35, 35, 50)(55 70, 75)
50  55
2
_
105
x
2
_
x
The value in between 50
and 55 is 52.5
_
x  52.5
The median is 52.5
The mode
The most common response. The value in the data set which appears the most.
e.g. Find the mode of the dataset 35, 35, 50, 55, 70, 75
The mode is 35 (it appears twice)
Key Skill 7: Understand the difference between discrete and continuous data
Numerical data gathered is either Discrete data or Continuous data.
Discrete Data
Numerical data that can only take certain values.
e.g. the number of pupils in a class (you can’t have half a pupil),
the number of visitors to a restaurant,
the number of cars parked in a car park.
Continuous Data
Numerical data that can take any value (within a certain range).
e.g. people’s height could be any value (within the range of human heights),
the time taken to run 100 metres (9.54 seconds, 9.538 seconds, 9.5382 seconds etc…)
the length of an attempt at the long jump (14.5 metres, 14.51 metres, 14.508 metres etc…)