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40
Number of Parking Tickets
0
10
20
30
Mon
da
y Tues
day
Wed
nes
d
ay
Thurs
day
Frid
ay
PictograPictogramsms
and and
Bar Bar ChartsCharts
Friday
Thursday
Wednesday
Tuesday
Monday
Line Line GraphsGraphs
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"
© Christine Crisp
Pictograms, Bar Charts Pictograms, Bar Charts and Line Graphsand Line Graphs
Data from the Office for National Statistics which is included in this presentation is reproduced under the terms of licence.
Diagrams are often used to show information from data.e.g. The following data set shows the
number of cars given parking tickets on a particular street on 5 weekdays.
Monday TuesdayWednesd
ayThursday Friday
20 20 5 35 40As always, the frequencies are numbers, but we don’t have numbers for the days of the week.
The data are qualitative (descriptions) instead of quantitative (quantities or numbers).
Both types of data can be shown in pictograms and bar charts.
Monday TuesdayWednesd
ayThursday Friday
20 5 35 40e.g. A pictogram of the data.
Friday
Thursday
Wednesday
Tuesday
Monday
Decide how many real cars are represented by a picture of a car.
Ans: 10
Key: = 10 carsThe diagram must have a title and key.
pictogram picture
Number of Parking Tickets
Number of Parking Tickets
20
There is very little difference between a pictogram and a bar chart.We replace the pictures with bars !
Friday
Thursday
Wednesday
Tuesday
Monday
Number of Parking Tickets
As before, we must have a title but instead of a key we have a scale.Bar charts are easier to draw using squared paper.
0 10 20 30 40
40
Number of Parking Tickets
0
10
20
30
Mon
da
y Tues
day
Wed
nes
d
ay
Thurs
day
Frid
ay
Friday
Thursday
Wednesday
Tuesday
Monday
Number of Parking Tickets
0 10 20 30 40
Bar charts are often drawn with the bars going up the page.
Friday
Thursday
Wednesday
Tuesday
Monday
Number of Parking Tickets
0 10 20 30 40
40
Nu
mb
er
of
Park
ing
Tic
kets 0
1020
30
Fri
day
Th
urs
da
yWed
nesd
ay
Tu
esd
ayM
on
da
y
Fri
day
Th
urs
da
yWed
nesd
ay
Tu
esd
ayM
on
da
y
Nu
mb
er
of
Park
ing
Tic
kets 0
1020
3040
To find the mean number of tickets issued per day, we sum the frequencies and divide by the number of days.
40
Number of Parking Tickets
0
10
20
30
Mon
da
y Tues
day
Wed
nes
d
ay
Thurs
day
Frid
ay
Friday
Thursday
Wednesday
Tuesday
Monday
Number of Parking Tickets
0 10 20 30 40
Bar charts are often drawn with the bars going up the page.
Friday
Thursday
Wednesday
Tuesday
Monday
Number of Parking Tickets
0 10 20 30 40
mean number of tickets issued per day= 20 + 20 + 5 + 35 +
40 5 = 24
Double, or dual, bar charts can be used to compare data. This chart compares
the way that boys and girls in a junior class travelled to school.
Fre
qu
en
cy
0
2
4
6
8
10
12
BusT
rai
n Taxi
Wal
kin
g
Methods of Transport to
School
Fre
qu
en
cy
BoysGirls
Answer the following:
(a) How many girls go by train?
(b)How many children go by taxi?
(c) What is the most popular way of getting to school?
Ans: (a) 2 (b) 4 (c)Walking
A line graph is mostly used when data are given at regular intervals of time. For example, times of day, months, or years.
Year
Number
(millions)
1991 15.1
1993 18.4
1995 19.2
1997 16.5
1999 14.8
2001 12.6
e.g. The table shows the total number of recorded crimes in England and Wales.
Source: Office for National Statistics: British Crime Survey, Home Office
Draw a line graph to display the data.
Solution: We plot the years on the x-axis (horizontally) and the number of crimes up the y-axis (vertically). The points are joined with straight line segments.
Year
Number
(millions)
1991 15.1
1993 18.4
1995 19.2
1997 16.5
1999 14.8
2001 12.61991
1993 1995
1997 1999
2001
Total Number of Crimes committed in England and
Wales
Year
Solution:
Tell your partner 2 things the graph tells you about the number of crimes.
x
x x
xx
x
• Between 1991 and 2001, most crimes occurred in 1995.• Crime decreased each year from 1995 to 2001. ( Other answers are possible. )
Nu
mb
er
(million
s)
Exercise
1. The diagram shows the spending by overseas tourists in parts of the U.K. in 2001.
SW England
Heart of England
Wales
Scotland
Area
Source: Office for National Statistics Key: = £100
million(a)How much was spent by the
tourists in (i) the Heart of England and (ii) Wales?(b)The figure for SW England was £450 000 000. How many pictures would show this?
Area
Scotland
Wales
Heart of England
SW England
Exercise
Source: Office for National Statistics Key: = £100 million
(a) (i) £700 million was spent in the Heart of England(ii) £250 million was spent in Wales.
Answers:
(b)4½ pictures are needed to show £450 000 000.
2. The diagram shows the estimates of fish stock in the North Sea in the 1970s and 1990s.
(a) Which type of fish stock increased between the 1970s and the 1990s?
(b)What was the estimate of the stock of cod in the 1970s?
Ans:
Ans: 800 000 ( 800 thousand ) tonnes
North Sea Fish Stocks
0
1000
2000
3000
Cod Herring Haddock
Frequency( thousands
of tonnes )
70's
90's
Source: Office for National Statistics
Herring
Qualitative data has descriptions instead of numbers.
SUMMARY
Pictograms and bar charts can be used to display qualitative and quantitative data.
e.g. days of the week, colours, transport methods.
Pictograms must have a title and a key. The key gives the frequency for each picture.
The lengths of the bars on a bar chart give the frequencies. Bar charts must have a title and a scale.
Line graphs have straight line segments joining the points. The x-axis often shows time.
A histogram is a bar graph that shows the frequency of data within equal intervals. There is no space between the bars in a histogram.
Course 2
Histograms
The table below shows the number of hours students watch TV in one week. Make a histogram of the data.
Additional Example 3: Making a Histogram
Step 1: Make a frequency table of the data. Be sure to use equal intervals.
Course 2
Histograms
6 ///
7 //// ////
8 ///
9 ////
1 //
2 ////
3 //// ////
4 //// /
5 //// ///
Number of Hours of TV
1–3
FrequencyNumber of Hours of TV
15
4–6 17
7–9 17
Additional Example 3 Continued
Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.
Course 2
Histograms
1–3
FrequencyNumber of Hours of TV
15
4–6 17
7–9 17
20
16
12
8
4
0
Additional Example 3 Continued
Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.
Course 2
Histograms
1–3
FrequencyNumber of Hours of TV
15
4–6 17
7–9 17
20
16
12
8
4
0
Additional Example 3 Continued
Step 4: Label the axes and give the graph a title.
Course 2
Histograms
1–3
FrequencyNumber of Hours of TV
15
4–6 17
7–9 17
20
16
12
8
4
01–3 4–6 7–9
Hours of Television Watched
Frequ
ency
Hours
The table below shows the number of hats a group of students own. Make a histogram of the data.
Try This: Example 3
Step 1: Make a frequency table of the data. Be sure to use equal intervals.
Course 2
Histograms
1–3
FrequencyNumber of Hats Owned
12
4–6 18
7–9 24
1 //
2 ////
3 //// /
4 //// /
5 //// ///
6 ////
7 //// /
8 //// ////
9 //// ////
Number of Hats Owned
Frequency
Try This: Example 3
Step 2: Choose an appropriate scale and interval for the vertical axis. The greatest value on the scale should be at least as great as the greatest frequency.
Course 2
Histograms
1–3
FrequencyNumber of Hats Owned
12
4–6 18
7–9 24
30
25
20
15
10
5
0
Try This: Example 3
Step 3: Draw a bar graph for each interval. The height of the bar is the frequency for that interval. Bars must touch but not overlap.
Course 2
Histograms
1–3
FrequencyNumber of Hats Owned
12
4–6 18
7–9 24
30
25
20
15
10
5
0
Try This: Example 3
Step 4: Label the axes and give the graph a title.
Course 2
Histograms
1–3
FrequencyNumber of Hats Owned
12
4–6 18
7–9 24
30
25
20
15
10
5
01–3 4–6 7–9
Number of Hats Owned
Frequ
ency
Number of Hats