STATISTIC FORM III
Statistics is the
practice or science of collecting and analyzing numerical data in large
quantities, especially for the purpose of inferring proportions in a whole from
those in a representative sample.
- Statistics is
the discipline that concerns the collection, organization, analysis,
interpretation and presentation of data.
- Statistics is a
branch of mathematics dealing with the collection, analysis, interpretation,
and presentation of masses of numerical data
- Statistics is
the science that deals with the collection, classification, analysis, and
interpretation of numerical facts or data, and that, by use of mathematical
theories of probability, imposes order and regularity on aggregates of more or
less disparate elements.
- Statistics is
an information based on a study of the number of times something happens or
is present, or other numerical facts.
- Statistics is the
study of collection, analysis, interpretation, presentation, and organization
of data. Data refers to crude or uninterrupted information.
- Statistics is the
study of methods of collecting, summarizing, analyzing and presenting data in a
clearand understandable way by using numbers.
Statistics
Data are exact
numerical facts collected systematically and arranged for a particular purpose.
Data may be obtained from official sources, government publications, ministry
bulletins and international bureau statistics.
Sources of Geographical
Data
There are two sources
of geographical data which include primary sources and secondary sources.
1. Primary Sources
of Geographical Data
These are the data
obtained directly from the field through questionnaires observation,
interviews, tests and focus group discussion.
2. Secondary
Sources of Geographical Data
These are the data
obtained from libraries, magazines, newspapres, published or unpublished
documents such as books, journals, maps and other public documents.
Types of Statistical
Data
1. Discrete Data:
are data which can not take any value within a given set but can only represent
a whole number like people and animals, cars, house, livestock, etc.
E.g: There were thirty students or thirty one students
2. Continuous
Data: these are data which can take any value within a set of a given number.
These values have fractions and decimal points. Continuous data include those
data whose values can be measured like temperature, altitude, height, etc.
E.g.: 25°C, 680m.
3. Individual
Data: these are data provide precise, specific and exact value for each
individual item in a sample given. Every individual represents its own value.
For instance in usongwe High School comprises of five streams A, B, C, D, E and
each stream has 45, 63, 42, 51, 51 students respectively. Each figure is thus
an exact value for a given class.
4. Grouped Data:
this represent a group of value or class which may fall under one
value or class in with no exact figures are quoted but where several values
fall within certain classes or groups.
Variable
A variable is anything
or characteristic that data may have, or an attribute which changes in value
under given conditions. Variables include population size, age, sex, altitude,
temperature and time. Variable can be classified into two major forms:
1. An independent
variable is a variable factor which influences the changes of other variables
or outcomes eg. Sex, year etc. it is expressed on the x-axis. The independent
variable is also known as manipulated variable.
2. A dependent
variable is an outcome or result that has been influenced by other
variables. A dependent variable does not influence or change other variables.
The dependent variable responds to independent variable. It is called dependent
because it “depends” on the independent variable. For example the higher the
attitude the lower the temperature and vise versa, for that reason increase or
decrease of temperature depends on attitude.
WAYS OF PRESENTING DATA
Data can be presented
in several ways. These include pictorical charts, block diagrams, tables,
graphs and maps. This study focuses on bar graphs and line graphs.
BAR GRAPHS AND LINE
GRAPHS
Threre are various
types of bar and line graphs used to present geographical data. The main bar
and line graphs include:
1. Simple bar and line
graphs
2. Grouped bar and line
graphs
3. Copmpound bar and
line graphs
4. Divergent bar and
line graph
A) LINE (LINEAR)
GRAPHS
Line graphs have unique
properties that distinguish them from other graphs.
The properties of line
graphs are as follows:
1. The graphs are drawn
by plotting a dependent variable against an independent
variable and points are
joined by a line.
2. The values on the
y-axis start at point zero.
General Procedures for
Drawing Line Graphs
1. Get the required
data for plotting the graph.
2. Identify the
independent and dependent variable. Statistically, the independent variables
are placed on the x-axis while the dependent variables are placed on the
y-axis.
3. Decide on the
vertical scale depending on the graph space and values of the independent
variable available.
4. Decide on the
horizontal spacing of the graph according to graph space available.
5. Draw and divide the
vertical and horizontal axes depending on the respective scales.
6. Plot and join the
points to get the graph.
7. Write the title of
the graph you have drawn.
8. Indicate the scale
of the graph.
9. Show the key for the
graph if need be.
Line Graphs can be
sub-divided into:
1. Simple line graphs
2. Group (comparatives)
line graphs
3. Compound line graphs
4. Divergent line
graphs
1. SIMPLE LINE
GRAPH
Presenting the
statistical data by a simple line graph is the most common and popular method.
The simple line graphs are easy to construct and interpret.
They have many uses
which include showing temperature, farm outputs, population, and mineral
production, among others.
Construction Procedure:
The graph can be drawn
after getting the required data. Consider the following table which shows the
average monthly temperature recorded in a certain weather station:
Average monthly
temperature for station X
The following
procedures may be used:
1. Identify the variables.
The dependent variable is temperature and the independent variable is months.
2. Determine a vertical
scale. Assume that the graph space available is 6 cm vertically. Vertical scale
= maximum value of the divided by the graph space available e.g. 30°C/6 cm =
5°C per centimetre. Therefore, in the vertical axis (xaxis), 1 cm will
represent 5°C
3. Determine the
horizontal scale (y-axis) depending on the available space. Let, for instance,
1 cm represent one month.
4. Draw both axes and
label them: y-axis for temperature and x-axis for months.
5. Plot the points and
join them by a smooth line to make a curve.
6. Insert the title and
scale.
Simple Line Graph
showing Monthly
Temperature for
Station X.
Scale
Vertical – 1 cm:5°C
Horizontal – 1 cm:1
month
Advantages of Simple
Line Graphs
1. They are easy to
draw, read and interpret.
2. They show specific
values of data, so if you are given one variable the other can easily be
determined.
3. They show patterns
in data clearly, meaning that they visibly show how one variable is affected by
the other as it increases of decreases.
4. They enable the
viewer to make predictions about the results of data. So they allow for
determination of intermediate or continuing values.
5. It is easy to read
the exact values against plotted points on straight line graphs.
6. A broken scale can
be used when the value starts at a large number.
Disadvantages of simple
line graphs
1. They can only be
used to show the data of one item over time.
2. One can change the
data of a line graph by not using consistent scales on the axis.
3. They can give a
wrong impression on the continuity of data even when there are periods
when data is not available.
4. They do not give a
clear visual impression of the actual quantities.
2. GROUP LINE
GRAPH
A group line graph is
also known by the following terms:
- Comparative line
graph
- Composite line graph
- Multiple line graph
- Polygraph
A group line graph
involves drawing more than one line on the same statistical graph. It shows the
relationship between sets of similar statistics for two or more items.
Usefulness of a Group
Line Graph
1. Comparing different
values or trends in two or more data variables.
2. Examining the
possibility of a relationship existing between the distributions of
a number of variables
over time.
3. Comparing the
distribution of the same variable at different places.
Construction:
The method of drawing a
group line graph is the same as for a simple line graph. Therefore, to draw
each single line in a group line graph, follow similar steps used for
construction of the simple line graph.
The following things
should be considered before drawing the graph:
1. The lines drawn
should not be uniform in colour, thickness, general appearance, etc (See the
graph below in which each line has a different colour).
2. The number of lines
that a graph can accommodate should not exceed 5, meaning that not more than 5
items should be compared in a single graph.
The following table
shows banana production (in tonnes) by three villages in Ingwe Division, Tarime
district. These data have been used to plot the group
(comparative) line
graph as shown below:
Banana production by
three villages
Group Line Graph
showing Maize production by
three villages between
2000 and 2002
Advantages of Group
Line Graph
1. The quantity of each
component is shown clearly by different line shadings.
2. Time and space are
saved since all the line graphs are drawn at ago as a
group.
Disadvantages of Group
Line Graph
1. The lines can be
overcrowded and hence become difficult to read and
interpret if many data
are involved.
2. It does not give a
clear visual impression of actual quantities.
3. COMPOUND LINE
GRAPH
A compound line graph
is used to analyse the total and the individual inputs of
the specific
commodities or economic sectors. The graph involves drawing
two or more lines, each
line corresponding to one item in a different year or
region. The items are
differentiated from each other or one another by
shading differently.
Construction
The table below is used
for construction of the graph. The table contains
hypothetical figures
for mineral exports between 2010 and 2012.
Procedure
1. Simplify the data to
make the presentation work easy by dividing each
value by 1000.
2. Add the values for
each year to get the cumulative export:
2010 = 10+16+20 = 46
2011 = 20+25+32 = 77
2012 = 25+35+40 =100
These values will be
used to determine the uppermost height of the graph.
They will also help
estimate the scale to be used. In case of the above data,
the highest value is
100. So if we want to use the scale of 1 cm to 1 tonne
(1000 tonnes in
reality), the uppermost height of our graph will be 100 cm
(see the graph drawn)
3. Plot the values for
mineral exports against years on a graph. Usually the
line graph for data with
the highest values is drawn first. Thus, first draw the
line graph for
tanzanite since it has the highest values, followed by that of gold
and finally diamond.
4. Draw the second line
graph above the first one to show the next
component. To get the
values for plotting the second line graph, add the
values of the first
item (in this case, tanzanite) to that of the second item
(gold) for each year,
thus:
2010 = 20+6 =36
2011 = 32+25 =57
2012 = 40+35 =75
5. Draw the line graph
for the last item (diamond) above that of the second
item. To get the values
for plotting this graph, add the values for the second
item to those of the
last item, thus:
2010 = 36+10 =46
2011 = 57+20 =67
2012 = 75+25 =100
6. Shade the component
parts between the line graphs using different
shadings
as shown.
7. Label the axes, show
the key and indicate the scale used to construct the
graph.
Compound Line Graph Mineral
Exports between 2010
and 2012
Advantages of Compound
Line Graph
1. Total values are shown
clearly and easily.
2. It gives good visual
impression.
3. Combining all graphs
in one saves time and space.
Disadvantages of
Compound Line Graph
1. Graph construction
is difficult and time-consuming.
2. It involves a lot of
calculations which are difficult and time-consuming.
3. It is difficult to
read and interpret the value for any one commodity for any
particular year.
3. DIVERGENT LINE
GRAPH
A divergent line graph
is a line graph which shows how variables deviate from
the mean. The mean is
represented by zero axis drawn horizontally across
the graph paper.
Construction
1. Sum up the values of
all items or commodities. 1000 + 1500 + 500 + 3000
= 6000
2. Calculate the
arithmetic mean (average) of the values. 6000/4 = 1500 Thus
the arithmetic mean =
1500
3. Calculate the
deviation from the mean of each value as shown in the table
below.
Deviation from the mean
value
4. Plot the graph using
the values of deviation from the mean; and remember
to include the
title and scale of the graph.
Disadvantages of simple
line graphs
1. They can only be
used to show the data of one item over time.
2. One can change the
data of a line graph by not using consistent scales on
the axis.
3. They can give a
wrong impression on the continuity of data even when
there are periods
when data is not available.
4. They do not give a
clear visual impression of the actual quantities.
2. GROUP LINE
GRAPH
A group line graph is
also known by the following terms:
- Comparative line
graph
- Composite line graph
- Multiple line graph
- Polygraph
A group line graph
involves drawing more than one line on the same statistical
graph. It shows the
relationship between sets of similar statistics for two or
more items.
Usefulness of a Group
Line Graph
1. Comparing different
values or trends in two or more data variables.
2. Examining the
possibility of a relationship existing between the distributions
of
a number of variables
over time.
3. Comparing the
distribution of the same variable at different places.
Construction:
The method of drawing a
group line graph is the same as for a simple line
graph. Therefore, to
draw each single line in a group line graph, follow similar
steps used for
construction of the simple line graph.
The following things
should be considered before drawing the graph:
1. The lines drawn
should not be uniform in colour, thickness, general
appearance, etc (See
the graph below in which each line has a different
colour).
2. The number of lines
that a graph can accommodate should not exceed 5,
meaning that not more
than 5 items should be compared in a single graph.
The following table
shows banana production (in tonnes) by three villages in
Ingwe Division, Tarime
district. These data have been used to plot the group
(comparative) line
graph as shown below:
Banana production by
three villages
Group Line Graph
showing Maize production by
three villages between
2000 and 2002
Advantages of Group
Line Graph
1. The quantity of each
component is shown clearly by different line shadings.
2. Time and space are
saved since all the line graphs are drawn at ago as a
group.
Disadvantages of Group
Line Graph
1. The lines can be
overcrowded and hence become difficult to read and
interpret if many data
are involved.
2. It does not give a
clear visual impression of actual quantities.
3. COMPOUND LINE
GRAPH
A compound line graph
is used to analyse the total and the individual inputs of
the specific
commodities or economic sectors. The graph involves drawing
two or more lines, each
line corresponding to one item in a different year or
region. The items are
differentiated from each other or one another by
shading differently.
Construction
The table below is used
for construction of the graph. The table contains
hypothetical figures
for mineral exports between 2010 and 2012.
Procedure
1. Simplify the data to
make the presentation work easy by dividing each
value by 1000.
2. Add the values for
each year to get the cumulative export:
2010 = 10+16+20 = 46
2011 = 20+25+32 = 77
2012 = 25+35+40 =100
These values will be
used to determine the uppermost height of the graph.
They will also help
estimate the scale to be used. In case of the above data,
the highest value is
100. So if we want to use the scale of 1 cm to 1 tonne
(1000 tonnes in
reality), the uppermost height of our graph will be 100 cm
(see the graph drawn)
3. Plot the values for
mineral exports against years on a graph. Usually the
line graph for data
with the highest values is drawn first. Thus, first draw the
line graph for
tanzanite since it has the highest values, followed by that of gold
and finally diamond.
4. Draw the second line
graph above the first one to show the next
component. To get the
values for plotting the second line graph, add the
values of the first
item (in this case, tanzanite) to that of the second item
(gold) for each year,
thus:
2010 = 20+6 =36
2011 = 32+25 =57
2012 = 40+35 =75
5. Draw the line graph
for the last item (diamond) above that of the second
item. To get the values
for plotting this graph, add the values for the second
item to those of the
last item, thus:
2010 = 36+10 =46
2011 = 57+20 =67
2012 = 75+25 =100
6. Shade the component
parts between the line graphs using different
shadings
as shown.
7. Label the axes, show
the key and indicate the scale used to construct the
graph.
Compound Line Graph Mineral
Exports between 2010
and 2012
Advantages of Compound
Line Graph
1. Total values are
shown clearly and easily.
2. It gives good visual
impression.
3. Combining all graphs
in one saves time and space.
Disadvantages of
Compound Line Graph
1. Graph construction
is difficult and time-consuming.
2. It involves a lot of
calculations which are difficult and time-consuming.
3. It is difficult to
read and interpret the value for any one commodity for any
particular year.
3. DIVERGENT LINE
GRAPH
A divergent line graph
is a line graph which shows how variables deviate from
the mean. The mean is
represented by zero axis drawn horizontally across
the graph paper.
Construction
1. Sum up the values of
all items or commodities. 1000 + 1500 + 500 + 3000
= 6000
2. Calculate the
arithmetic mean (average) of the values. 6000/4 = 1500 Thus
the arithmetic mean =
1500
3. Calculate the
deviation from the mean of each value as shown in the table
below.
Deviation from the mean
value
4. Plot the graph using
the values of deviation from the mean; and remember
to include the
title and scale of the graph.
1. Simple bar graphs
2. Group or comparative
bar graphs
3. Compound bar graphs
4. Divergent bar graphs
1. SIMPLE BAR
GRAPH
A simple bar graph is
drawn to show a single item per bar. It mainly represents simple data.Consider
the data in the table below which shows the value of sisal exported by Tanzania
between 1900 and 1993:
Construction
1. Choose the
appropriate scale. However, note that the table below is not drawn to scale –
it was drawn using the computer. All hand-drawn graphs must indicate the scale
used. For, example, in our graph below, we might have chosen 1 cm to represent
10,000 tones, in which case we could obtain the values 5, 10, 15, 20 and 25
that we could have used to plot the graph.
2. Draw the axes and
insert the bars. Note that all the bars must have the same width and spacing.
3. Shade the bars
uniformly by using shade, lines, crosses, dots, etc.
4. Insert vertical and
horizontal scales and the title.
Simple Bar
Graph showing Tanzania sisal export
Scale: 1 cm to 50,000
tonnes
Advantages of a Simple
Bar Graph
1. It is simple to
construct, read and interpret.
2. It has a good visual
impression.
3. It can be used to
compare how the amount of an item varies from time to time.
Disadvantages of a
Simple Bar Graph
1. It is limited to
only one item or commodity and hence not suitable for massive data.
2. Not suitable for
continuous data such as temperature.
2. GROUP BAR GRAPH
A comparative/group bar
graph consists of several bars drawn side by side on the same chart for the
purpose of comparison. The technique involves grouping of bars in a chart. The
graph can be used to show how production of certain commodities varies each
year.
Construction:
The procedure for
construction of the comparative bar graph is similar to that of drawing the
simple bar graph except that the simple bar graph contains a single bar while
the comparative bar graph comprises of multiple bars.
Consider the data in
the table below, showing agricultural production in metric tonnes.
The graph for the data
is as shown below.
Group (comparative) Bar
Graph showing
Crop Yields in ‘000 kg
(1986 - 1988)
Advantages of a Group
Bar Graph
1. The total values are
expressed well for illustration of points.
2. It is easy to
construct, read and interpret.
3. The importance of
each component is shown clearly.
Disadvantages of a
Group Bar Graph
1. It is difficult to
compare the totals of each item/component.
2. Trends such as fall
and rise cannot be shown easily.
3. COMPOUND BAR
GRAPH
Compound/divided bar
graph is a method of data presentation that involves
construction of bars
which are divided into segments to show both the
individual and
cumulative values of items. The length of each segment
represents the
contribution of an individual item in the total length while that of
the whole bar
represents the total (cumulative) value of the dierent items in
each group.
Construction
1. Get the data needed
for presentation. For example, consider the table
below, which shows the
number of tourists who visited the named Tanzania
National Parks from
1998 to 2002.
2. Simplify the data
(to make the presentation work easy) by dividing each
value by 10,000. Then
add the values to get the total for each year. The
simplified data are as
shown in the table below.
3. Determine the scale
of the bar length based on the highest total value. In
this case, the highest
total value is 68 (20 + 20 + 10 + 18). Recall the
construction of the
compound line graph! If we choose 1 cm to represent 1
tourist (10,000
tourists in reality), then the length of the tallest bar will be 68
cm. Note that the
maximum height of a graph for each year equals the
cumulative total values
for each year (i.e. 43, 46, 48, 59, 68).
4. Decide on the bar
spacing, for example, 1 cm apart.
5. Draw the axes and
label them.
6. Start by drawing
bars that represent the highest values.
7. The first sets of
bars to be drawn are those that represent the highest
values. On top of
these, the second highest segments are drawn. The last
segments to be drawn
are those with the lowest values in general.
8. To make it easy to
follow the rise and fall of individual values, a soft line
could be drawn across
bars to separate individual segments.
9. Colour or shade the
segments to improve the appearance and simplify
interpretation.
10. Inset the scales,
key and title.
Compound (divided) Bar
Graphs showing
Tourist Visits in 0’000
(1998 - 2002)
Advantages of Compound
(divided) Bar Graph
1. It is easy to read
and interpret as the totals are clearly shown.
2. It gives a clear
visual impression of the total values.
3. It clearly shows the
rise and fall in the grand total values.
Disadvantages of
Compound (divided) Bar Graph
1. The values of
individual segments above the first set are difficult to
establish because they
don’t start at zero. To get the correct values of the top
segments, you have to
add the figures, which is difficult for someone not well
equipped with
statistical skills.
2. The graph is very
difficult to construct and interpret.
3. It is not easy to
represent a large number of components as this would
involve very long bars
with many segments.
4. DIVERGENT BAR
GRAPH
A divergent bar graph
is a graph which shows the uctuation of individual items
from the mean.
Construction
1. Calculate the
arithmetic mean (average) of the items.
2. Subtract the mean
from each item.
3. Draw the graph using
the resulting values.
4. Insert the scale and
title of the graph.
The data below show the
enrolment of Form One students at Mara Secondary
School from 1980–1985.
Study the table and present the data by a divergent
bar graph.
Procedure
1. Find the arithmetic mean:
2. Subtract the mean
from each item:
3. Choose a suitable
scale and construct the graph using the obtained values
(X – ).
Divergent Bar Graph
showing
Student Enrollment (1980-1985)
Advantages of Divergent
Bar Graph
1. Fluctuation in
values, which helps to detect the problem in general terms, is
shown.
2. It is important for
comparison of positives and negatives.
3. Profit (success) or
loss (failure) can easily be deduced.
4. They are simple to
construct, read and interpret.
Disadvantages of
Divergent Bar Graph
1. Graph construction
is time-consuming since it involves many steps.
2. The calculations
involved may be difficult to someone who is poor at
mathematics.
3. It is limited to
analysis of only one variable.
5. PIE
CHARTS OR DIVIDED CIRCLES
A divided circle is
also known as pie chart, circle chart or pie graph. The chart
involves dividing the
circle into “pie slices” to represent and show relative
sizes of data. The size
of each slice or segment is always proportional to the
value it represents.
Divided circles can appear in two forms:
1. Simple divided
circles.
2. Proportional divided
circles.
A simple divided circle
involves a single set of data whereas the proportional
divided circle involves
more than one set of data such that the circles will be
proportional to the
total quantity that each circle represents.
SIMPLE DIVIDED CIRCLE
Construction:
1. Obtain the data to
work on. Study this hypothetical record
showing enrolment
of Form One students in selected Secondary Schools
in Tarime
District:
A table showing student
enrolment in selected schools in Tarime District
2. Calculate the total
number of students as shown in the table.
3. Calculate the angle
in a circle that would represent the number of students
enrolled in each
school. For example, 85 out of 456 students enrolled in
Nyansincha Secondary
School will be represented in the circle by a segment
with an angle of 85/456
×630 = 67 degrees.This will give the following results:
4. Draw a circle of a
reasonable size.
5. Using a protractor,
draw a radius from the 6 o’clock mark to the centre of
the circle.
6. Starting with the
largest segment representing a specific component,
measure and draw its
angle from the centre of the circle.
7. Do the same for
other components in ascending order.
8. Divide a circle into
segments according to the sizes of the angles.
9. Shade the segments
and write the title and key of the drawn graph.
Pie Chart/Divided
Circle showing Student
Enrolment in Selected
Secondary Schools in
Tarime District
Advantages of Divided
Circles
1. It is easy to
compare components as they are represented by angles.
2. Analysis and
interpretation of data is easy.
3. It is easy to assess
the proportion of individual components against the
total.
4. Construction of this
graphical representation is relatively simple.
5. It is easy to
determine the value of each component since it is indicated on
each segment.
6. Visual impression of
the individual components is clear and facilitates the
understanding of the
information in the data.
Disadvantages of
Divided Circles
1. It is time-consuming
because it involves a lot of calculations.
2. The represented
actual values remain hidden as the values shown on the
faces of the segments
may be in percentages.
3. Where the range of
data is large and involves small and big values,
accurate construction
of the chart is difficult.
4. When the values of
data set vary slightly, it is difficult to visualize the
proportional
differences between values (as it is the case in the pie chart
above).
The Importance of
Statistics to the User
Statistics is important
in geography because of the following reasons:
1. It enables the
geographers to handle large sets of data and summarize
them in a way that can
be easily understood.
2. It can also enable
the geographers to make comparisons between
geographical phenomena,
e.g. to compare the amount of rainfall and
agriculture production
or population distribution in different regions, etc.
3. Statistics
translates data into mathematical ways which make the
application of
quantitative techniques
possible.
4. It enables the
geographers to store the information in forms of numbers,
graphs, tables, charts,
etc.
5. Statistics give
precise rather than generalized information. This offers a lot
of satisfaction to the
user.
6. Statistics is very
useful for planning at local and national levels. For
example, statistics on
census can be used to plan for social services
Source from MSOMI BORA.
