Lecture 7

Discrete symbol maps

1. Definition:
Maps which use symbols to represent data.
- qualitative or quantitative data
--- (so : qualitative or quantitative symbols)
- symbols usually refer to points
- sometimes refer to an area

2. Geometric Symbols
- circle, cross, triangle, square, star... many choices
- easy to draw and duplicate
- colour or pattern expand choice or highlight special symbols
- rarely look like what they represent, so map readers must use the legend

3. Pictorial Symbols
- person, house, ship, raindrop, tree... no limit to choice
- harder to draw
- colour or pattern expand choice or highlight special symbols
- can look like what they represent, so easy to interpret (but still need a legend)

---Note: letters and numbers can also be used as map symbols.

4. Dot Distribution Maps
- a base map with a large number of small dots.
- each dot represents a specific number of items ('dot value').
- must be stated on map.
- common for population maps (not only for people)
- and for agricultural production (both dispersed widely across regions).
- where dots are densest, population is greatest.
- easy visualization of distribution.

- disadvantage - if data has great variation, dot value is hard to select.
--- if too small (5 people per dot), dense areas become solid black, dots cannot be counted.
--- if too large (100,000 per dot), sparse areas are missed or their values combined or exaggerated.
--- if you use 1000 people per dot:
------ 300 dots needed for London, 3000 for Toronto.
------ Solid black, not possible to count and estimate population.
--- if you use 1000 people per dot:
------ what do you do with a group of small villages of 150 to 300 people each?
------ Any solution is misleading.
--- if you use 100,000 people per dot:
------ better for Toronto, useless for northern Ontario.
- problem solved sometimes by using proportional circles to replace biggest concentrations (e.g. big cities)

5. Multiple Symbols
- Many different kinds of symbol representing many different kinds of object.
- Common for maps of agricultural or mineral production.
- qualitative (nominal) data, qualitative (different shape) symbols.
- if many different kinds of symbol, pictorial or letter symbols used to reduce reliance on the legend (but still need legend).

- examples:
- pictures of agricultural products
- chemical symbols for elemental ores (Pb for lead, etc.)
- keep symbols about the same size - no suggestion of proportional symbols.

6. Repeating Symbols
- Identical symbols repeated to indicate a value.
- Each symbol represents a certain number of items.
- example:
- one human figure represents 1 million population
- draw 9 figures in Ontario, 6 in Quebec, 3 in B.C.
- sometimes subdivided to help with lesser values
--- half a person represents 500,000 people
--- half a figure drawn in Manitoba

Proportional Symbols

7. Proportional Symbols
- size varies with value to be represented
- 'size' may refer to one or two dimensions of the symbol
- one: height, length or width; two: area

linear proportionality:
- height of column or line made proportional to (e.g.) annual rainfall.
--- base of line at location of measurement.
- width of line represents traffic along a route
--- position of line indicates location of the route - a 'flow' map

area proportionality:
- area of symbol is proportional to city population.
--- centre of symbol placed at location of city.

- recall formuli for areas of simple shapes:
--- circle area: p r² --- (r = radius)
--- square area: l² --- (l = side length)
--- rectangle area: base x height
--- triangle area: 1/2 base x height

- simplest approach: calculate side length for a square,
- then use that result for one dimension of any shape.

Proportional symbol examples

1. Example of Linear Proportionality (column map)

STEP 1: select M = maximum permitted symbol height
--- (depending on map size, design, number of symbols)
STEP 2: identify V = largest value in data set (or nearby convenient round number)
STEP 3: for each value = v in the data set,
column height / maximum height = value for that column / largest value
--- or: height / M = v / V
--- or: height = M (v / V)
STEP 4: plug in values, calculate heights.
--- use a spreadsheet if you find it convenient.
STEP 5: draw a set of columns with equal widths but using calculated heights.

STEP 6: add three symbols for convenient round numbers near smallest, middle and largest values in data set.
--- Use these for legend.
- remember to label legend with original values, not square roots.

2. Flow Maps
- use the same procedure as for the column map, but apply it to the width of a line, not the length.

- see instructions in Lab 10 section.

3. Example of Area Proportionality (square symbol)

STEP 1: select L = largest permitted square side length
STEP 2: take square roots of all values in data set
STEP 3: identify V = largest value in step 2 (or nearby convenient round number)
STEP 4: for each value = v in step 2,
side length / maximum length = value for that symbol / largest value
--- or: length / L = v / V
--- or: length = L (v / V)
STEP 5: use these side lengths to control sizes of symbols.
STEP 6: add three symbols for convenient round numbers near smallest, middle and largest values in data set.
--- Use these for legend.
- remember to label legend with original values, not square roots.

If you want to use a circle symbol, use calculated length as diameter.

Numerical example:
STEP 1: choose L = largest square length = 2 cm
STEP 2: take square root of all values
STEP 3: V = largest value in step 2 = 1342 - (original value = 1.8 million people)
STEP 4: for a value v = 632.5 from step 2 - (original value = 400,000 people)
- length / L = v / V
- length / 2 = 632.5 / 1342
- length = 2 x 632.5 / 1342 = 0.94 cm

so draw square with side length 0.94 cm

check:

- 2 cm represents 1.8 million people
- 0.94 cm represents 400,000 people
- 400,000 is just under 1/4 of 1.8 million
- 0.94 cm is just under 1/2 of 2 cm
- symbol has about 1/2 the side length so about 1/4 the area
--- so AREAS really are proportional to original values.

8. Divided Symbols
- symbols divided into parts to show subdivisions of data
- usually done with geometric symbols

- one style of symbol:
--- circle represents a province.
--- drawn within province on base map
------ or use leader line: thin line connecting symbol to correct location.
--- sector blacked out to indicate the proportion of the workforce in part-time jobs.
------ A 'pie' diagram used as a map symbol.

- formula: angle of sector / 360^o = value of subdivision / total value

- or: angle of sector = 360^o x value of subdivision / total value

- example:
- symbol represents workforce of 250,000 people
- subdivision: 50,000 people in part-time jobs
--- so the sector size = 360^o x 50,000 / 250,000
--- = 360^o x 0.2
--- = 72^o

- Note: to make the diameter of each circle proportional to its value in the workforce dataset, see the 'proportional symbol' section above.

- another style of symbol:
- column represents a province.
- base of column drawn within province on base map.
- height of column proportional to workforce
- lower part blacked out to indicate the proportion of workforce in part-time jobs.

- formula: height of part / total height = value of subdivision / total value

- or: height of part = total height x value of subdivision / total value

- example: column represents workforce of 250,000 people
- vertical scale chosen to be 1 cm to 50,000 people
- total height of column = 5 cm
- subdivision: 80,000 people in part-time jobs
--- part height = total height x 80,000 / 250,000 cm
--- = 5 x 0.32 cm
--- = 1.6 cm

- so you draw a 5 cm high column (narrow rectangle) with the bottom half made darker.