As it has been introduced in the chapter one; the numerical data after being collected, summarized and analyzed; are presented to provide pictorial view (visual idea).
One of the useful ways for presenting the numerical facts is by diagrams. It is thus; statistical diagrams designed to illustrate values of geographical items and in turn allow quantitative analysis.
The most useful statistical diagrams for the illustration of quantitative data include the following.
- Pie chart
- Proportional semi divided circles
- Divided rectangle
- Proportional circles
- Scatter diagram
- Wind rose
- Polar chart
PIE CHART
Pie chart is also known as divided circle or pie graph. It is a method of drawing a circle of any convenient size divided proportionally into a number of segments to show the values of items in percentages.
The number of segments the circle is divided into depends on the number of items whose have to appear in the circle. The proportional size of segments is determined by the degree values of the percentages.
Construction of pie chart
Consider the given data below for world production of cocoa by countries in 1968.
Country | Production |
Brazil | 1,936,297 |
Ghana | 4,042,988 |
Nigeria | 2,308,066 |
Ecuador | 805,499 |
Cameroun | 1,270,211 |
Ivory coast | 1,796,883 |
Others | 33,304,430 |
Procedures:-
(a) Total values determination.
1,936,297 + 4,042,988 + 2,308,066 + 805,499 + 1,270,211 + 1,796,883 + 33,304,430 = 15,490,374
(b) Percentage values determination
(c) Degrees of the percentage values determination:
Country | Production | X% | X^{0} |
Brazil | 1,936,297 | 12.5% | 4^{0} |
Ghana | 4,042,988 | 26.1% | 93.6^{0} |
Nigeria | 2,308,066 | 14.9% | 53.6^{0} |
Ecuador | 805,499 | 5.2% | 18.7^{0} |
Cameroun | 1,270,211 | 5.2% | 29.5^{0} |
Ivory coast | 1,796,883 | 11.6% | 41.8^{0} |
Others | 33,304,430 | 21.5% | 77.4^{0} |
(d) The circle of any convenient size should be drawn. It should be divided into proportional segments with respect to the computed degree values. Too small circle is not required.
It is thus; the pie chart for the data appears as follow.
Strengths of the pie chart
The method is more pleasing to eye and it is one among the most popular methods in statistics for data representation.
The values given by the method are more simplified as appear in percentages.
It allows the easy making of quantitative analysis.
Setbacks of the pie chart
It does not give the absolute values of items represented
It consumes much of time to prepare. Hence it is tedious enough.
It needs high skill to prepare it
A problem may arise in selecting the varied shade of textures.
PROPORTIONAL SEMI DIVIDED CIRCLE
This pictorial method, involves the drawing of two semi circles linked to one another and each is proportional to the total quantity represented.
Each semi circle is proportionally divided into segments and the number of segments the semi circle is made to have, depends on the number of items. In making the segments in the semi circle, 180^{0} is used as the total degree for each semi cycle.
The method is very useful in making comparison of items for two major cases like dates or places.
Construction of the proportional semi divided circles
Consider the following tabled data showing motor vehicles production for passengers and commercial in the industrialized nations.
W. total | USA | W. Germany | Japan | U.K. | France | ||
Comm | 6530 | 1896 | 241 | 2052 | 409 | 242 | 750 |
Passe | 21720 | 8222 | 2862 | 2055 | 1816 | 1832 | 280 |
Procedure:-
(a) Find the total values for each variable
Commercial: 1896 + 241 + 2052 + 409 + 242 + 750 + 940 = 6530
Passengers: 8222 + 2862 + 2055 + 1816 + 1832 + 280 + 4653 = 21720
(b) Angle determination of the segments
Commercial:-
(c) Passengers.
(d) Estimation of the diameters of the two proportional semi circles. It is much up on specific scale. The scale is developed by proposing specific value to be represented by 1cm. Le say 1cm should represent 20000 motor vehicles.
Thus the proportional semi divided circle for the data given appears as follow:-
WORLD PRODUCTION OF MOTOR VEHICLES BY COUNTRIES (000)
Diameter scale:-
1cm represents 2000 motor vehicles.
Merits of the semi divided proportional circles
It is useful technique for showing comparison of item values for two major cases
It provides visual idea
It allows the making of quantitative analysis
Setbacks of the proportional semi divided circles
It needs high skill to extract actual values from the diagram
It consumes much time to prepare
It needs high skill to be prepared
It encounters a problem shade textures selection
DIVIDED RECTANGLE
It is one among the most useful and versatile method of statistical presentation of data. However it is not frequently used.
By this method, the total quantity is presented by a rectangle which is then sub divided to represent the constituent parts.
Depending on the function, the divided rectangle is of two types including:-
- Simple divided rectangle
- Compound divided rectangle
SIMPLE DIVIDED RECTANGLE
It is a rectangle drawn to have a length proportional to the total quality represented, then divided into proportional segments to show the values of the cases.
Construction of the simple divided rectangle
Consider the following data of coffee production in Tanzania in ‘000’ tons in 1980.
REGION | PRODUCTION |
Arusha | 9 |
Kilimanjaro | 10 |
Bukoba | 18 |
Ruvuma | 11 |
Mbeya | 7 |
Tanga | 5 |
(a) Determine the scale value to be used in drawing the rectangle.
Hence; 1 cm represents 6 tons.
(b) Determine the length of the values along the rectangle
Thus; the simple divided rectangle for the given data appears as follow:-
Simple divided rectangle coffee production in ‘000’ tons from 1980 to 1985
COMPOUND DIVIDED RECTANGLE
By the compound divided rectangle, each proportional strip in the rectangle is also proportionally divided to show further information of the cases represented.
This is drawn with two scales. One scale is for horizontal dimension, and it is designated as the horizontal scale; the other is for the vertical dimension and is designated as vertical scale.
It is much better for the two scales graduated in separate values. The horizontal scale is absolute values and the vertical scale be in percentage.
Example:-
Consider the given data below showing land use partners for the six village:-
COUNTRIES | SIZE LANDUSE OF TOTAL AREA ‘000’ KM^{2} | |||
Westland | Pasture | Arable | forestry | |
Ruvu Darajani | 166.5 | 27 | 31.5 | 225 |
Vigwaza | 94.4 | – | 40.4 | 202.2 |
Buyuni | 226.8 | – | 32.4 | 64.8 |
Kidogozero | 7.7 | 5.2 | 21.5 | 8.6 |
Visezi | 8.5 | 13.3 | 6.8 | 5.4 |
Kitonga | 8.8 | 8.2 | 10 | 7 |
Procedure:-
(a) Cumulative values determination.
Ruvu Darajani:- 166.5 + 27 + 31.5 + 225 = 450
Vigwaza:- 94.4 + 40.4 + 202.2 = 337
Buyuni:- 226.8 + 32.4 + 64.8 = 324
Kidogezero:- 7.7 + 5.2 + 21.5 + 8.6 = 43
Visezi:- 8.5 + 13.3 + 6.8 + 5.4 = 34
Kitonga:- 8.8 + 8.2 + 10 + 7 = 34
(b) The percentage values determination
· Ruvu Darajani:-
· Vigwaza:-
·Buyuni:-
· Kidogezero:-
· Kitonga:-
(c) Scale determination
(e) Horizontal scale
Hence; Horizontal scale: 1 cm represents 125%
(f) Vertical scale
Merits of the divided rectangle
It is useful method for showing cumulative values
It is more illustrative as it provides visual idea to the users in statistics
It allows the easy making of quantitative analysis
The data represented by compound divided graph can also be represented by percentage bar graph.
Set backs of the divided rectangle
It is not much pleasing to people
It consumes much time to prepare especially the compound divided rectangle
It needs high skill to prepare the compound divided rectangle
It needs high skill to prepare the compound divided rectangle
It is much less used for statistical data representation
A problem can be encountered in selecting the varied textures provided items are numerous.
PROPORTIONAL CIRCLES
It is diagram with circles whose size proportional to the quantity represented. The area size of a circle is calculated by the following application:-
But in our case; is ignored. The radius varies with the quantity to be represented. Hence; proportional circles are drawn with radii proportional to the square root of the quantity represented.
Construction of proportional circles
Consider the given data below:-
Hydroelectricity production for some stations in country X.
HEP Station | Production in MW |
A | 100 |
B | 144 |
C | 255 |
D | 400 |
E | 625 |
Procedure:
(a) The values should be arranged in ascending or descending order. i.e. 100,144, 255, 400, 625.
(b) Find the square roots of the values.
√100 = 10
√255 = 15
√400 = 20
√625 = 25
(c) Estimate the radius value scale to be used for all proportional circles. In the estimation, propose the highest radius to be used. Then the highest square root should be divided by the proposed highest radius.
Thus; 1 cm to 5 square root.
(d) The proportional circles should be drawn accordingly.
In drawing the proportional circles; the following procedure should be followed.
The circles are drawn proportionally to the quantity represented depending on the scale that has been decided.
The two perpendicular lines should be drawn to follow the arrangement of the circles.
The central line should be drawn through all circles.
PROPORTIONAL CIRCLES SHOWING HEP PRODUCTION FOR THE STATIONS
Note
The proportional circles can be drawn on a map. This is done under the recommendation of showing values of places which appear on the map. The proportional circles on the map, sometimes may overlap. This is not a problem.
But if it is possible, the best should be tried to minimize the size of the circles. One of the ways is to minimize the scale size.
Consider the map with proportional circles on the next page.
Advantages of proportional circles
It is a good method of comparing absolute values
The proportional circles give good visual impression
Disadvantages of the proportional circles
It is much tedious in construction
It becomes difficult to determine the exact values from the circles.
SCATTER DIAGRAM
This method is also known as scatter graph. It is a statistical diagram designed to show correlation between two types of data. The diagram is made to have two lines axis. The vertical axis is used to show the values for the dependent variable; while the horizontal axis is used to show the values for independent variable.
On the diagram; a straight line is drawn to follow the distribution of dots.
If the plotted dots appear closer to straight line, indicates greater correlation
If the plotted dots appear widely scattered from the line indicates low or no correlation.
Construction of the scatter diagram
Consider the given data below showing the amount of rainfall at varied altitudes.
Altitude (m) | Rainfall (mm). |
500 | 600 |
600 | 800 |
700 | 1200 |
800 | 1500 |
900 | 1700 |
1000 | 2000 |
1100 | 2400 |
Procedure:
(a) Identify the variables
·Dependent variable – Rainfall distribution values
·Independent variable – Altitude
(b)Estimation of both vertical and Horizontal scales
Hence; VS 1cm represents 500mm
Hence; HS 1cm represents 250m
According to scatter diagram above, the plotted dots are much closer to the line, This shows greater positive correlation between rainfall and altitudes. i.e. rainfall greatly influenced by altitude.
WIND ROSE
It is a statistical diagram designed to show the number values of wind blow frequencies per varied direction and speed in a given month as it was recorded at a certain weather station.
Wind rose is of two types including simple and compound wind roses.
SIMPLE WIND ROSE
Simple wind rose only shows number of wind blow frequencies per directions. It is made to have octagon sides or a circle of any convenient size. If octagon used; on each side, a rectangle of equal or varied length to others is drawn to represent the directions from which winds were blowing.
If rectangles are made to have equal length, in each, small lines established to represent the number of wind blow frequencies. If are made of not equal length, each whose length is made proportional to the number of wind blow frequencies. The number of days which didn’t experience wind blow (calm days) written in a circle inside the octagon.
Example:
Construct the simple wind rose to represent the following data.
Wind blow frequencies at X weather station for the month of June.
DIRECTION | N | NE | E | SE | S | SW | W | NW |
WIND Fq | 5 | 4 | 4 | 1 | 3 | 4 | 3 |
WIND ROSE FOR X WEATHER STATION
COMPOUND WIND ROSE
Compound wind rose is employed to show the average wind blow frequencies per varied direction and speed commonly in percentage of a given month for station weather station.
Example:
Construct the compound wind rose to present the following data.
Wind blow frequencies at X weather station for the month of June in percentages.
Wind speed/Direction | N | NE | E | SE | S | SW | W | NW |
Less than 4kph | 2 | 2 | 3 | 3 | 4 | 2 | 5 | 4 |
4 – 12 kph | 3 | 4 | 2 | 5 | 2 | 3 | 4 | 2 |
13 – 22 kph | 2 | 2 | 1 | 1 | 3 | 2 | 2 | 3 |
Total | 11 | 10 | 9 | 11 | 11 | 10 | 15 | 11 |
Calm days = 18%
The compound wind rose for the given data is constructed as follow.
· Scale value determination
Hence; 1cm represents 3% frequency
Thus; the wind rose appears as follow:-
Advantages of wind rose
It gives a visual impression of wind frequencies
It is relatively easy to construct and takes a short time provided a scale is well assessed
It is easy to understand information represented.
Disadvantages of a wind rose
Numerical values not easily extracted as it needs measuring and calculating using the given scale.
One cannot know the exact time or day when wind blew from a particular, direction since the wind rose is a summary of the conditions over a period of time.
The pattern of wind blow over a given period cannot easily be seen from the diagram.
POLAR CHART
The graph is also known as circular graph or clock graph. It is a graph in circular form designed to have bars and circular line to show two attributes whose values appear in vaired unit.
It is basically employed to illustrate the amount of temperature and rainfall together in a year. However polar chart can also be used in other cases of distribution recorded in a year.
For the case of showing climatic records, polar chart employ the use of both bars and line to illustrate rainfall and temperature values respectively.
The circle is divided into twelve equi angular radii.
Construction of the circular graph
The following tabled data show the climatic condition for certain weather station in Jerusalem.
Month | J | F | M | A | M | J | J | A | S | O | N | D |
Temp ^{o}C | 8 | 9.1 | 12.2 | 17 | 21 | 22 | 23 | 24 | 23 | 21 | 17 | 12 |
Rain mm | 150 | 160 | 70 | 30 | 18 | 00 | 00 | 00 | 00 | 22 | 80 | 90 |
Steps
Estimation of the value scales to be used.
Thus, the value scale for rain fall is 1cm to 40 mm
Hence; the temperature vertical scale; 1cm represents 5^{0}c
The polar chart has to be drawn as follow:-
Strength as of the circular graph
It is useful graphical method for showing the distribution values of climate
It is more illustrative, as it provides visual idea to the users in statistics
It allows the easy making of quantitative analysis
Setbacks of the circular graph
It needs high skill to make quantitative analysis from the Graph
It is time consuming graphical method in construction
Needs high skill to construct the graph