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GEOGRAPHY FORM THREE WORK.
TOPIC ONE: STATISTICAL MEHODS
By Prof. Ogoti Robert Maxwell
- Methods of presenting statistical data that we learn in form three are: Compound/ cumulative bar graphs. Proportional circles Pie charts Proportional divided circles. 1. Compound/ Cumulative Bar Graphs.
- Comprise of one or more bars drawn vertically or horizontally with each bar subdivided so that each portion represents a component of the data that makes the whole.
- Where two or more bars are drawn, each bar is separated with an equal space between them.
- Suitable for presenting data depicting the total value of several items.
Example. Kcse 2017: The table below shows the number of visitors in ‘000’ to selected national parks in Kenya for the years 2006 to 2008.
PARK/ YEAR 2006 2007 2008 NAIROBI 102 93 92 AMBOSELI 153 156 82 TSAVO 354 372 182 LAKE NAKURU 327 347 138 TOTAL 946 968 497
Draw a compound bar graph to represent the number of visitors to selected national parks in Kenya. Use the scale of 1cm to represent 100,000 visitors.
Interpretation of Compound bar Graphs.
- Observe the trend of the bars. Look for the total of the variables of each bar in the period given.
- Compute the trend of an individual variable against the successive totals of each bar.
- Comment on the trend of each variable.
- From the interpretation, suggest possible reasons to explain the trend of the variables obtained.
NOTE: The following interpretation can be deduce from the drawn compound bar graph; Kenya received more tourists in the year 2007. Kenya received few tourists in the year 2008. Tsavo national parks received highest number of tourists for the years 2006 to
Lake Nakuru is the second national park visited by many tourists. Tsavo national park received highest number of tourists in 2007. Nairobi national park received lowest total number of tourists. Number of tourists who visited Nairobi National park reduced from 2006 to
Draw proportional circles to represent the total export earnings during the period of 2012 to
- Use diameter method.
Solution. Round off the totals.
YEAR TOTALS ROUND OFF
Analysis and interpretation of proportional circles – kcse 2018 i.) The total export values for the selected crops was highest in 2012. ii.) The total export value had a decline for the consecutive years. iii.) 2014 registered the lowest export value. iv.) Total exports value for the three years has very little significant difference.
b). Use of Circles with Areas Proportional to the total values.
- The proportional circles may be drawn by drawing circles whose areas are proportional to the square roots of the absolute values.
- Find the square roots of each set of data.
- Choose a suitable scale for the use in calculating the different radii of the circles. The scale should neither be too big nor too small. This is to ensure that the sizes of the circles is convenient.
- Then draw circles using the different radii.
Example. The table below shows total sugar production by five factories in Kenya from 2015 to 2018.
FACTORIES 2015 2016 2017 2018
MUMIAS 192,556 212,455 249,550 262,
NZOIA 124,500 144,660 150,500 182,
CHEMELIL 120,460 139,550 140,400 142,
SONY 100,500 110,624 120,340 136,
WEST KENYA 50,600 521,240 55,650 574,
TOTAL 588,616 659,429 716,440 781,
Draw proportional circles to represent the total sugar production by factories in Kenya during the period of 2015 to 2018. Use area method.
Solution.
- Get the square root of the total value for each year i.e.
Year 2015: √ 588,616 = 767.
- Choose a suitable scale to get radius i.e. 1cm represent 400 units
400 = 1.9cm
YEAR TOTAL VALUE SQUARE ROOT VALUE
RADIUS (cm)
2015 588,616 767.2 1.9cm 2016 659,429 812.1 2.0cm 2017 716,440 846.4 2.1cm 2018 781,885 884.2 2.2cm
Draw proportional circles to represent the total population of some counties in the lake region of Kenya. a) Use diameter method. b) Use area method.
3. PIE CHARTS/ DIVIDED CIRCLES/ PIE GRAPHS.
- These are circles drawn and subdivided to represent statistical data.
- Each segment of the circle represents a given component of the data.
- The size of the segment is equivalent to the quantity of the value of the component.
Types of pie charts. Simple pie charts. Proportional divided circles.
A simple Pie Chart (Divided Circle).
- This involves drawing a circle of a convenient size representing a complete set of recorded data.
- The circle is then sub-divided with each segment representing a component of the set data.
- Each component is calculated as a percentage of the whole and then converted to degrees.
Example. Kcse 2020: The table below shows estimated production of selected crops in Kenya in 2013.
Crop Production (Number of bags). Maize 38,900, Beans 6,100, Sorghum 1,800, Millet 700, Source: Economic Survey of Kenya, 2014.
Using a radius of 5cm, draw a pie chart to represent the data in the table above. Show your calculations.
iv.) Draw the circles using the scale in (ii) above then insert the details just like in simple pie charts, labelling each component. In each of the circles, shade the same components in the same way as above. v.) Give the proportional divided circles a title and a key.
Example. The table below shows causes of death in countries X, Y and Z in 2017. Country HIV/AIDs Road accidents Drug abuse Total X 10,000 2,000 2,400 14, Y 3,000 4,100 1,000 8, Z 500 270 130 900
Draw proportional divided circles.
Solution.
Sizes of the circles: √ 14,400 = 120
√ 8,100 = 90
√ 900 = 30
Scale: let 1cm represent 20.
Radius of circle for country X = 120 20 = 6cm
Radius of circle for country Y = 90 20 = 4.5cm
Radius of circle for country Z = 30 20 = 1.5cm
COUNTRY X
HIV/AIDs : 10,000 x 360⁰ = 250⁰ 14,
Road accidents : 2,000 x 360⁰ = 50⁰ 14,
Drug abuse: 2,400 x 360⁰ = 60⁰ 14,
COUNTRY Y
HIV/AIDs : 3,000 x 360⁰ = 133⁰ 8,
Road accidents : 4,100 x 360⁰ = 182⁰ 8,
Drug abuse: 1,000 x 360⁰ = 45⁰ 8,
COUNTRY Z
HIV/AIDs : 500 x 360⁰ = 200⁰ 900
Road accidents : 270 x 360⁰ = 108⁰ 900
Drug abuse: 130 x 360⁰ = 52⁰ 900
Interpretation of Proportional Divided Circles
- The circles represent the proportion of the variable in each category.
- The segments in each circle describe the nature of the variable.
- In the proportional circles given HIV/AIDS which presently has no cure is the leading cause of death is the countries X, Y and Z.
- The size of the circle represent the total number of deaths, country X has the highest number of deaths followed by countries Y and Z.
Advantages of proportional divided circles. Easy to draw/ construct. Easy to read/ interpret. Gives clear visual impression.
Disadvantages of proportional divided circles. Time consuming while constructing/ calculating. Values cannot be read at a glance. Represents a few variables/ items.
Assignment. The table below shows beverage production in three counties in Kenya in 2021.
County Coffee Cocoa Tea Total Kericho 1,000 800 700 2500 Muranga 225 600 400 1225 Nyeri 250 50 100 400
Draw proportional divided circles.
“END OF TOPIC ONE”
MAPWORK
PART ONE: INTRODUCTION.
- A map is a representation of the whole or part of the earth surface on a flat surface like a piece of paper, a wall, clothes e.t.c.
- Map work is the ability to read/ interpret/ analyse/ draw maps for better understanding of relief, drainage and various human activities on maps.
Types of maps.
a) Topographical map.
- It is one which shows a selected number of physical and human features and their distribution on the earth surface.
- It is drawn by specially trained people called cartographers.
- It is drawn from air or aerial photographs and ground surveys.
- Topographical maps are used to answer question six of geography paper one (312/1).
Characteristics of topographical maps.
They are drawn to scale. They are medium scale map sizes (1:50,000). They have a map title and map name. They have marginal information. They represent a small area such as a village/location. They depict physical features (relief, drainage, vegetation) and human activities (social and economic).
b) Atlas/ projected map.
- It is a collection of many maps bound in one volume, resembling a book showing different physical features and human activities.
Characteristics of Atlas Maps. They are used to represent a large area such as a country/continent/World in a small sheet of paper. They are drawn on a very small scale. They may represent specific or general information in an area.
c) Sketch/ outline map.
- Refers to rough drawings showing specific information which the user requires to see e.g. A sketch map of Africa showing distribution of Major Fold Mountains.
- Title of the map/ sheet title; Usually printed on top left hand side of the map extract containing scale and country e.g. Kenya 1:50000 or East Africa 1: Type of information contained on the sheet title; Region where the map was developed. The ratio scale.
- Map sheet number/ map edition/ map series; They are mostly found in a small box on top right corner of the map provided. Sheet number identifies the map sheet from the other sheets in the same group e.g. 115/1- Yimbo Map edition shows the year when the map was published/ printed e.g. 1971 Map series shows the group of maps to which a particular map sheet belongs e.g. Y73 (D.O.S 423)
Series Y73(D.O.S.423) Sheet 115/ Edition 1971
How to identify a map.
i. Map series e.g. Y73(D.O.S 423) ii. Map sheet e.g. 115/ iii. Map edition e.g. 1971 iv. Map name e.g. YIMBO Scale
- It is a ration between the map distance and the corresponding ground distance.
- Types of scales include: Representative Fraction scale/Ratio scale. Linear scale. Statement scale e.g. 1cm represent 0.5km
- On topographical maps, scales are expressed in two forms only that is linear scale and Representative fraction scale.
- Types of scales used in the map – kcse 2021
Linear scale e.g. 0 1 2 3 4 5 km Representative fraction (RF)/ Ratio scale e.g. 1: 50,
- Conversion of scale to statement scale – kcse 2023 RF 1: 1km 100,000cm ?? 50,000cm 50,000cm X 1km = 0.5km or ½ km 100, 000cm Therefore, statement scale = 1cm represent ½ km or 0.5km
- Contour interval; It is the difference in value between two consecutive/ adjacent contours. Found at the key written as V.I= 20m or V.I= 50ft
- Index to adjoining sheets; It is a square containing nine small squares. The area covered by the map is shown at the centre and the bordering regions. Always write the sheet number then the name e.g. an area bordering Funyula to the south is 131/1- Ganjala 116/ KISOKO
BUMAYENGA
BUMALA
NAKHASIKO
FUNYULA
NAMALO
BUDALANGI
GANJALA
NAMASALI
The compass direction;
Magnetic north True north
Grid north
Magnetic variation Grid variation
Six grid reference.
Give the first two Easting readings then estimate the third digit i.e. 547 Give the first two Northing readings then estimate the third digit i.e. 453 The six-figure Grid Reference of point P is 547453.
Use a ruler/a set square or graph paper to subdivide the Grid Square into 10 equal parts for both Easting and Northing. This is to provide accurate reading for the third values for easting and northing. Examples.
Solution. Points Four G.R Six G.R A 1990 19 5 90 5 B 2094 20 2 94 8 C 2192 21 8 92 2
D 2393 23 6 93 8 E 2492 24 4 92 0 F 2690 26 8 90 8 G 2590 25 2 90 8
- Naming features found on the grid reference – kcse 2023
E
River Road E Huts/ houses/ settlement
Eldoret W E
S
N
W E
Kitale
S Direction of Kitale from Eldoret is South West. Direction of Eldoret from Kitale is North East.
- Bearing is the direction of a place given in form of an angle/ degrees e.g. N
Eldoret W E
S
N
W E
Kitale
S
