Statistical Maps and Graphical Representation Alıştırma Soruları — JAMB UTME

Soru 1Soru →

A divided bar chart of total length $15\text{ cm}$ is constructed to illustrate the land use distribution of an agricultural zone covering a total area of $120,000\text{ hectares}$ . If livestock grazing occupies $32,000\text{ hectares}$ of this land, what is the length in $\text{cm}$ of the bar segment representing livestock grazing?

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Cevap: 4

Cevap

The length of the bar segment representing livestock grazing is

4\text{ cm}

.

The correct answer of

4\text{ cm}

is obtained by finding the fraction of total land devoted to grazing (

\frac{32,000}{120,000} = \frac{4}{15}

) and scaling it by the total bar length of

15\text{ cm}

.

Adım Adım Çözüm

1

Calculate the proportion of the land area used for livestock grazing

Proportion =

\frac{32,000}{120,000} = \frac{4}{15} \approx 0.2667

Divided bar charts represent component parts proportionally relative to the whole dataset.

2

Multiply the proportion by the total bar length to find the length of the segment

Segment length =

\frac{4}{15} \times 15\text{ cm} = 4\text{ cm}

The total length of the bar represents

100\%

of the total area, so each sub-component's length is proportional to its contribution.

Anahtar Kavram

Calculating component segment lengths for divided bar charts using proportional ratios

Soru 2Soru →

A pie chart is constructed to illustrate the revenue distribution of agricultural crop exports from a region. If the total export revenue is $\$800\text{ million}$ and Cocoa accounts for $\$360\text{ million}$ , what is the angular size of the sector representing Cocoa on the pie chart?

45^\circ

97.2^\circ

162^\circ

180^\circ

Cevabı ve açıklamayı göster

Cevap: $162^\circ$

Cevap

The sector representing Cocoa has an angular size of

162^\circ

.

The total revenue of

\$800\text{ million}

corresponds to a full circle of

360^\circ

. Cocoa's revenue of

\$360\text{ million}

forms

\frac{360}{800} = 0.45

of the total. Multiplying this ratio by

360^\circ

gives

162^\circ

.

Adım Adım Çözüm

1

Calculate the proportion of total export revenue generated by Cocoa.

Proportion =

\frac{\$360\text{ million}}{\$800\text{ million}} = 0.45

Determining the fractional share of the target category from the total dataset.

2

Convert the proportion into degrees for a pie chart sector.

Angle =

0.45 \times 360^\circ = 162^\circ

A complete circle subtends

360^\circ

, so multiplying the fractional component by

360^\circ

yields the exact sector angle.

Anahtar Kavram

Pie Chart Sector Angle Calculation

Soru 3Soru →

A statistical table shows the annual agricultural crop production for a region in Nigeria as follows:

Crop	Production (metric tonnes)
Cocoa	$540$
Oil Palm	$360$
Rubber	$180$
Groundnut	$120$

If this data is to be represented using a pie chart, what is the exact difference between the central angle allocated to Cocoa and the combined central angle allocated to Rubber and Groundnut?

72^\circ

90^\circ

144^\circ

162^\circ

Cevabı ve açıklamayı göster

Cevap: $72^\circ$

Cevap

The difference between the central angle allocated to Cocoa and the combined central angle allocated to Rubber and Groundnut is

72^\circ

.

The total commodity output equals

1200

tonnes. The sector angle for Cocoa is calculated as

\frac{540}{1200} \times 360^\circ = 162^\circ

. The combined tonnage for Rubber and Groundnut is

180 + 120 = 300

tonnes, giving a combined angle of

\frac{300}{1200} \times 360^\circ = 90^\circ

. The difference between these two values is

162^\circ - 90^\circ = 72^\circ

.

Adım Adım Çözüm

1

Calculate the total crop production

\text{Total} = 540 + 360 + 180 + 120 = 1200\text{ metric tonnes}

The total dataset value is required to determine the proportional weight of each commodity.

2

Calculate the central sector angle for Cocoa

\text{Angle}_{\text{Cocoa}} = \left(\frac{540}{1200}\right) \times 360^\circ = 0.45 \times 360^\circ = 162^\circ

A pie chart represents total data as a

360^\circ

circle.

3

Calculate the combined central sector angle for Rubber and Groundnut

\text{Combined Production} = 180 + 120 = 300\text{ metric tonnes}

;

\text{Angle}_{\text{Combined}} = \left(\frac{300}{1200}\right) \times 360^\circ = 0.25 \times 360^\circ = 90^\circ

Summing the metric tonnage of the two minor crops allows direct conversion to their aggregated sector angle.

4

Determine the difference between the angles

162^\circ - 90^\circ = 72^\circ

Subtracting the combined angle from the primary crop angle yields the required angular difference.

Anahtar Kavram

Calculation of Sector Angles for Pie Charts

Soru 4Soru →

Match each type of statistical map or graphical representation on the left with its most appropriate geographical application on the right.

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Cevabı ve açıklamayı göster

Cevap

Choropleth map matches displaying population density using shaded administrative areas; Dot map matches showing absolute spatial distribution of population using point symbols; Flow map matches illustrating volume and direction of cargo or passenger movements; Pie chart matches showing percentage component breakdown of a total statistical value.

Each mapping technique is specifically designed for a particular data format: Choropleth maps represent area-based densities, Dot maps present absolute point distributions, Flow maps display movement volumes, and Pie charts represent percentage proportions of a total.

Adım Adım Çözüm

1

Analyze Choropleth map characteristics

Matches displaying population density using shaded administrative areas

Choropleth maps use graded shading over administrative units to convey continuous density or ratio data.

2

Analyze Dot map characteristics

Matches showing absolute spatial distribution of population using point symbols

Dot maps represent raw numerical quantities distributed spatially using point symbols.

3

Analyze Flow map characteristics

Matches illustrating volume and direction of cargo or passenger movements

Flow diagrams display dynamic movements along paths with width scaled to quantity.

4

Analyze Pie chart characteristics

Matches showing percentage component breakdown of a total statistical value

Pie charts show proportional sub-divisions of 360 degrees corresponding to 100% of a dataset.

Anahtar Kavram

Selection and Functions of Statistical Maps and Diagrams

Soru 5Soru →

A geographer is constructing a statistical map using proportional circles to represent agricultural output across regions. Region A produced $100{}000\text{ metric tonnes}$ of cassava and is drawn with a circle radius of $1.5\text{ cm}$ . If Region B produced $400{}000\text{ metric tonnes}$ of cassava, what is the correct radius required for the circle representing Region B?

3.0\text{ cm}

6.0\text{ cm}

0.75\text{ cm}

4.5\text{ cm}

Cevabı ve açıklamayı göster

Cevap: $3.0\text{ cm}$

Cevap

The radius required for the circle representing Region B is

3.0\text{ cm}

.

For proportional circle maps, the visual area of each symbol must be directly proportional to the magnitude of the data represented (

A \propto V

). Since the area of a circle is

A = \pi r^2

, the radius

r

is proportional to the square root of the statistical value (

r \propto \sqrt{V}

). The output ratio between Region B and Region A is

400{}000 / 100{}000 = 4

. The square root of this ratio gives a radius scale factor of

\sqrt{4} = 2

. Multiplying Region A's circle radius of

1.5\text{ cm}

by

2

gives

3.0\text{ cm}

.

Adım Adım Çözüm

1

Calculate the ratio of the quantities represented by the two regions

Data Value Ratio =

\frac{400{}000}{100{}000} = 4

Determining how many times larger Region B's output is compared to Region A.

2

Apply the proportional symbol area scaling formula (

r \propto \sqrt{V}

)

Radius Scale Factor =

\sqrt{4} = 2

Because a circle's area is proportional to the statistical value (

A \propto V

), the radius must scale with the square root of the value ratio.

3

Calculate the required radius for Region B

Radius =

1.5\text{ cm} \times 2 = 3.0\text{ cm}

Multiplying the base radius of Region A by the radius scale factor.

Anahtar Kavram

Proportional Symbol Map Scaling (Square Root Radius Rule)

Soru 6Soru →

In practical geography, cartographers select specific statistical mapping techniques based on data characteristics, spatial continuity, and quantitative representation rules. Match each statistical mapping technique on the left with its defining cartographic principle or limitation on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Choropleth Map pairs with shading predefined administrative units based on average density ranges. Isopleth Map pairs with using continuous isolines joining places of equal value. Flow Map pairs with employing bands or vectors of proportional width for directional movement volume. Dot Map pairs with using uniform point symbols representing fixed quantitative values.

Each mapping technique corresponds directly to its spatial data type and cartographic construction method: Choropleth maps shade administrative units according to calculated density intervals; Isopleth maps utilize isolines to show continuous spatial variations across continuous surfaces; Flow maps draw lines whose widths vary proportionally with trade or migration volumes; Dot maps display discrete totals by placing point symbols of fixed values across regions.

Adım Adım Çözüm

1

Analyze Choropleth mapping principles

Identified that choropleth maps rely on average density ratios mapped to administrative regions with shaded fill gradients.

Administrative boundary shading is the core structural element of choropleth cartography.

2

Analyze Isopleth mapping principles

Identified that isopleths join equal values across a continuous phenomenon field using interpolated isolines.

Continuous data representation like temperature or pressure requires isoline interpolation.

3

Analyze Flow mapping principles

Identified that flow maps connect origins and destinations with proportional line widths.

Movement of goods, trade, or migrants across geographical space is measured along directional pathways.

4

Analyze Dot mapping principles

Identified that dot maps assign a unit value per point to represent absolute discrete counts.

Dot maps effectively demonstrate spatial clustering without falsely placing dots at exact coordinates.

Anahtar Kavram

Cartographic characteristics, rules, and limitations of statistical maps

Tahmini Süre:2m 0s

Soru 7Soru →

Match each statistical mapping technique on the left with the cartographic representation principle and data type it utilizes on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Dot Map pairs with uniform point symbols representing discrete distributions; Choropleth Map pairs with shading intensities within administrative boundaries for average densities; Flow Map pairs with varying line thickness depicting volume of movement; Isopleth Map pairs with lines connecting points of equal value for continuous phenomena.

Each mapping technique matches its primary cartographic design function: dot maps represent absolute discrete quantities using uniform point symbols; choropleth maps represent spatial densities using shading aggregated inside administrative units; flow maps convey directional movement and volume via proportional line widths; and isopleth maps depict continuous environmental variables by linking points of equal magnitude with isolines.

Adım Adım Çözüm

1

Identify the data symbol type for Dot Maps.

Dot maps use point symbols of fixed value to represent discrete counts across a region.

This establishes the relationship between Dot Map and uniform point symbols.

2

Identify the spatial boundary and shading rule for Choropleth Maps.

Choropleth maps rely on predetermined administrative boundaries filled with graded shading to show average ratios or densities.

This pairs Choropleth Map with administrative unit shading.

3

Analyze how dynamic movement data is represented cartographically.

Flow maps use proportional line widths along travel channels to quantify movements like trade or migration.

This pairs Flow Map with varying line thickness along movement paths.

4

Examine continuous spatial surface mapping using contour-like lines.

Isopleth maps interpolate continuous distributions (e.g., isotherms, isobars) by connecting equal numerical values.

This matches Isopleth Map with lines of equal value across surfaces.

Anahtar Kavram

Cartographic principles of statistical maps and quantitative spatial data representation

Soru 8Soru →

Pair each geographical representation method listed below with the specific type of spatial data or phenomenon it is best suited to display.

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Cevabı ve açıklamayı göster

Cevap

Dot Map matches with discrete point distribution using uniform symbols; Choropleth Map matches with administrative data shown via progressive shading; Flow Line Map matches with direction and volume of movement; Isoline Map matches with continuous environmental variables.

Each mapping technique aligns directly with specific spatial data properties: Dot Maps depict discrete distributions using uniform symbols; Choropleth Maps summarize regional averages per administrative unit using shading; Flow Line Maps measure linear movement volume; and Isoline Maps map continuous environmental fields by connecting points of equal value.

Adım Adım Çözüm

1

Analyze the characteristic of a Dot Map.

Dot maps utilize uniform point symbols where each dot represents a fixed quantitative value to show spatial distribution.

This method is suitable for discrete distributions such as population or crops.

2

Analyze the characteristic of a Choropleth Map.

Choropleth maps apply varying shades to administrative divisions according to average data values.

Shading intensities correspond to ranges of density or ratios within defined political boundaries.

3

Analyze the characteristic of a Flow Line Map.

Flow line maps use arrows or bands of varying thickness along travel routes.

The line width directly indicates the volume of movement such as trade or passenger traffic.

4

Analyze the characteristic of an Isoline Map.

Isoline maps connect geographic locations having identical numeric values.

This technique represents continuous spatial fields such as elevation, temperature, or rainfall.

Anahtar Kavram

Cartographic selection and statistical mapping representations in practical geography.

Soru 9Soru →

In quantitative cartography, proportional circles are constructed such that the surface area of each circle is directly proportional to the statistical quantity being represented. On a demographic map of West Africa, a city with a population of $4,000,000$ is drawn using a proportional circle with a radius of $3.0\text{ cm}$ . Which of the following is the correct radius required to represent a neighboring metropolitan city with a population of $16,000,000$ on the same map?

6.0\text{ cm}

12.0\text{ cm}

4.0\text{ cm}

1.5\text{ cm}

Cevabı ve açıklamayı göster

Cevap: $6.0\text{ cm}$

Cevap

The correct radius required to represent the city is

6.0\text{ cm}

.

The area of a proportional circle represents the statistical quantity (

A \propto P

). Because circle area is calculated as

\pi r^2

, the radius

r

must vary with the square root of the population (

r \propto \sqrt{P}

). The population ratio between the two cities is

\frac{16,000,000}{4,000,000} = 4

. Taking the square root gives

\sqrt{4} = 2

. Multiplying the initial radius of

3.0\text{ cm}

by

2

yields the accurate radius of

6.0\text{ cm}

.

Adım Adım Çözüm

1

Identify the relationship between statistical data and proportional circle dimensions.

The area of a circle

A = \pi r^2

is proportional to the statistical quantity

P

. Therefore,

r \propto \sqrt{P}

.

Cartographic principles require symbol areas, not linear radii, to reflect statistical magnitudes.

2

Set up the ratio between the radii and the square root of populations for both cities.

\frac{r_2}{r_1} = \sqrt{\frac{P_2}{P_1}}

Using ratios eliminates the proportionality constant

k

and simplifies calculation.

3

Substitute given values into the ratio formula.

\frac{r_2}{3.0} = \sqrt{\frac{16,000,000}{4,000,000}} = \sqrt{4} = 2

Simplifying the population fraction yields a square root factor of 2.

4

Calculate the unknown radius

r_2

.

r_2 = 3.0 \times 2 = 6.0\text{ cm}

Multiplying the baseline radius by the scale factor yields the required circle radius.

Anahtar Kavram

Square root scaling rule for proportional circle radii in statistical maps

Soru 10Soru →

A cartographer constructs a quantitative dot map to represent the distribution of livestock across a region. On the map, a total of $64$ dots represent a total population of $160,000$ sheep. If Province X has a sheep population of $35,000$ , how many dots should be plotted to represent Province X on this map?

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Cevap: 14

Cevap

14 dots are required to represent Province X.

To find the dot count for Province X, first determine the scale value of a single dot:

\frac{160,000\text{ sheep}}{64\text{ dots}} = 2,500\text{ sheep per dot}

. Next, divide the population of Province X by the dot value:

\frac{35,000\text{ sheep}}{2,500\text{ sheep/dot}} = 14\text{ dots}

.

Adım Adım Çözüm

1

Determine the quantity represented by one dot.

Each dot represents

2,500

sheep.

Dividing the overall sheep population (

160,000

) by the total number of dots (

64

) establishes the dot value.

2

Calculate the number of dots for Province X.

14 dots.

Dividing the provincial population (

35,000

) by the single-dot value (

2,500

) yields the exact number of dots required for visual representation.

Anahtar Kavram

Dot Map Scale and Quantifier Calculation

Soru 11Soru →

Relate each statistical mapping technique on the left to its governing cartographic principle or inherent analytical limitation on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Choropleth mapping corresponds to shading pre-defined administrative units with potential area-size visual bias; Isopleth mapping connects points of equal value across continuous surfaces via interpolation; Dot density mapping utilizes uniform point symbols to portray spatial density without exact coordinates; Flow line mapping varies line thickness along routes to illustrate movement volume.

Each statistical mapping method follows specific cartographic logic: Choropleth maps shade administrative zones; Isopleth maps connect continuous equal-value interpolated lines; Dot density maps use uniform dots to illustrate distribution without pinpointing exact locations; and Flow line maps scale line thickness to show movement volume along transit corridors.

Adım Adım Çözüm

1

Analyze the structural characteristics and limitations of Choropleth maps.

Identified that choropleth maps rely on administrative boundaries and quantitative shading, which can visually overemphasize larger geographical areas.

Choropleth mapping groups data into discrete areal classes defined by political or administrative boundaries.

2

Examine the continuous surface requirements for Isopleth maps.

Matched isopleths to lines connecting equal values calculated through interpolation of point measurements across space.

Isopleths represent continuous spatial phenomena (such as rainfall or elevation) rather than bounded areal counts.

3

Evaluate the spatial representation rules of Dot density maps.

Determined that dots represent aggregated quantities within an area and do not denote exact physical addresses or locations.

Dot maps distribute dots randomly within enumeration zones to convey density while maintaining uniform dot size.

4

Assess the visual metric used in Flow line maps.

Linked flow maps to variable line widths representing traffic, cargo, or population movement along specific pathways.

Flow lines use vector width proportional to magnitude to signify spatial interaction intensity.

Anahtar Kavram

Classification, principles, and limitations of thematic statistical maps

Soru 12Soru →

Match each statistical mapping technique listed on the left with the specific spatial phenomenon or cartographic data representation it is best suited to display on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Choropleth mapping pairs with density ratios displayed within predefined administrative unit boundaries. Dot distribution mapping pairs with absolute population numbers or livestock distributions using fixed quantitative point symbols. Isopleth mapping pairs with continuous spatial phenomena such as mean annual precipitation or temperature gradients. Flow line mapping pairs with volume, direction, and movement routes of international trade cargo or passenger traffic.

Choropleth mapping is designed for administrative ratio data; dot distribution mapping visually renders absolute discrete counts; isopleth mapping connects lines of equal continuous values; and flow line mapping depicts direction and volume of movement along transport routes.

Adım Adım Çözüm

1

Identify the data characteristic of Choropleth mapping.

It relies on spatial units (states/districts) to display derived ratios/densities via shading.

Administrative boundary categorization is the defining feature of choropleth technique.

2

Identify the data characteristic of Dot distribution mapping.

It uses dots representing absolute quantities (e.g., 1 dot = 1,000 cattle) to depict spatial density.

Point-based quantitative representations accurately show spatial clustering of discrete counts.

3

Identify the data characteristic of Isopleth mapping.

It connects points of equal value over continuous surfaces like atmospheric pressure, elevation, or temperature.

Isopleths require smooth, continuous spatial data distributions rather than abrupt administrative boundaries.

4

Identify the data characteristic of Flow line mapping.

It represents linear movements with line width scaled to movement volume.

Flow lines are specialized for network movement and transportation dynamics.

Anahtar Kavram

Selection of Statistical Maps and Graphical Representation Methods

Soru 13Soru →

A geography student constructs a pie chart to illustrate the annual export earnings of agricultural commodities from a region. The total value of all exports is $\text{\$}480\text{ million}$ , with oil palm products accounting for $\text{\$}108\text{ million}$ . What is the central angle, in degrees, of the sector representing oil palm products?

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Cevap: 81

Cevap

The central angle of the sector representing oil palm products is

81^\circ

.

The correct answer is obtained by finding the component share of the total value (108 / 480 = 0.225) and multiplying by 360 degrees, yielding an angle of 81 degrees.

Adım Adım Çözüm

1

Calculate the fractional proportion of the specific component relative to the total data value

\frac{108}{480} = 0.225

A sector in a pie chart represents a fractional part of the total statistical value.

2

Convert the calculated proportion into degrees of a circle

0.225 \times 360^\circ = 81^\circ

A full pie chart circle contains

360^\circ

, so multiplying the component proportion by

360^\circ

gives its angular representation.

Anahtar Kavram

Calculating Sector Angles in Pie Charts

Soru 14Soru →

A cartographer is tasked with displaying population density across different administrative districts in a state by applying varying intensities of shading, where darker shades represent higher densities. Which statistical mapping technique is being described, and what is a primary cartographic limitation of this method?

Isopleth map, which inverts the numerical scale ratio when plotting continuous lines of equal value across administrative boundaries.

Choropleth map, which falsely assumes a uniform distribution of the phenomenon throughout each administrative unit.

Proportional symbol map, which incorrectly assumes that doubling the map's linear scale doubles the represented surface area.

Flow map, which misattributes depositional statistics to upper course geographical regions.

Cevabı ve açıklamayı göster

Cevap: Choropleth map, which falsely assumes a uniform distribution of the phenomenon throughout each administrative unit.

Cevap

The correct mapping technique is a choropleth map, whose primary limitation is creating an illusion of uniform population distribution across the entire administrative unit.

A choropleth map uses tonal shading or graduated colors applied to specific boundary units (such as states or districts) to display average values or densities. A major limitation of this technique is the false assumption that population density is evenly distributed across the entire area inside each boundary.

Adım Adım Çözüm

1

Identify the mapping technique based on the spatial data display method.

The technique using varying shades or patterns applied within pre-defined administrative boundaries to show density or average values is a choropleth map.

Choropleth mapping relies on quantitative areal data aggregated by spatial units such as states or districts.

2

Analyze the cartographic limitations of choropleth maps.

Choropleth shading covers entire administrative zones evenly, giving the false impression that values are uniform throughout each zone.

Administrative boundaries rarely align with natural transitions in population density or spatial phenomena.

Anahtar Kavram

Choropleth Mapping and Spatial Data Generalization

Statistical Maps and Graphical Representation

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