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A. Map Scale

B. Measurement Scales

C. Accuracy, Precision, and also Monumental Digits

D. Classification, Simplification and also Symbolization of Data

A. Map Scale

Map range is the connection between a unit of size on a map and also the corresponding length on the ground. We will certainly usage principles of map scale throughout the course, so it will certainly pay you to research this section very closely.

You are watching: A map scaled at 1:75,000 is considered to be which of the following?

1. Types of Map Scales

We deserve to relate map and also ground through 3 different forms of range. Verbal range expresses in words a relationship in between a map distance and a ground distance. Usually it is along the lines of:

 

One inch represents 16 miles.

 

Here it is implied that the one inch is on the map, and also that one inch represents 16 miles on the ground. Verbal scales are frequently found on well-known atlases and also maps.

The second type of range is a graphic range, or bar range. This reflects directly on the map the matching ground distance. For example:

 

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The third form of range is a representative fraction, or ratio scale. Compared to the first two, it is the the majority of abstract, but also the many flexible. A representative fractivity, or RF, reflects the partnership in between among any kind of unit on the map and one of the exact same unit on the ground. RFs might be presented as an actual fractivity, for instance 1/24,000, but are generally composed through a colon, as in 1:24,000. In this instance, one unit of any length (one mm, one cm, one inch, one foot, and so on.) on the map represents 24,000 of those exact same devices on the ground (24,000 mm, 24,000 cm, 24,000", 24,000", and so on.). The RF is versatile bereason you are not tied to any certain units. You might occupational in any type of unit you pick, either metric, English, or various other.

The RF is a dubbed a fraction because it is just that--a portion that mirrors how much the actual people is reduced to fit on the map. A great comparichild is often made with scale models of automobiles or aircraft. A 1/32-design of an auto is 1/3second as big as the actual auto. In the exact same means, a 1:100,000-scale map is 1/100,000th as large as the ground location displayed on the map.

A connected concept is that of tiny range versus large scale. Geographers usage these terms in a different way than many people. A big scale map is where the RF is reasonably huge. A 1:1200 map is therefore larger range than a 1:1,000,000 map. The 1:1,000,000 map would commonly be called a little range map. This is true also though the 1:1,000,000 map would certainly present a a lot larger area than the 1:1200 map.

Here is a rule of thumb for dimension of range by RF:

 

 

Size of ScaleRepresentative Franction (RF)
Large Scale1:25,000 or larger
Medium Scale1:1,000,000 to 1:25,000
Small Scale1:1,000,000 or smaller

 

Of course, what is little or huge range is relative. I noticed a surveying text (Brinker & Wolf, 1984) that classed anypoint smaller sized than 1:12,000 as small scale -- surveyors seldom work with anypoint smaller sized than this.

The large/small range terminology have the right to come to be confutilizing when talking about big versus small locations. If you are talking about a phenomenon that occurs throughout a big region, it is tempting to say it"s a massive phenomenon (e.g., "the woodland blight is a massive disease"). But given that the map that would show this would certainly be small-range, it is much better to usage a different term to avoid confusion. My favorite is "broad-scale."

Many maps encompass two or even all three forms of scales. USGS topographic maps have actually both bar scales and also RFs.

2. Converting Between Scale Types

If you are given one type of range, you need to have the ability to derive or construct any type of of the other two. This takes some exercise, and some troubles are contained in your lab exercises. Some examples are offered listed below.

A vital action in doing any kind of type of convariation that involves differing devices is to include the units in the trouble itself. You can then cancel the systems by multiplying or splitting. This method you prevent ending up being puzzled around which convariation determinants to use and how to use them.

Verbal Scale to RF

The key right here is to compose the verbal range as a portion, then convert so that both numerator and also denominator have the exact same units, and also the numerator has actually a 1.

 

(a) Convert verbal range of "1" to 18 miles" to RF

 

 

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or 1:1,140,000.

Notice that the resulting fraction is rounded so that the RF does not indicate even more accuracy than the original precision warranted.

 

(b) Convert verbal range of "15 cm to 1 km" to RF

 

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or 1:6700.

In many conversions you have the right to save procedures if you remember added equivalencies.

For instance, in (a) over, we might have actually provided the fact that 1 mile = 63,360 inches to skip a action.

Verbal Scale to Graphic Scale

Usually this is a fairly basic task if the map offers us reasonable units in the verbal range. We have the right to usage the verbal range prefer a fraction to transform the ground distance to map distance.

 

(c) Convert verbal scale of "1 cm to 14 km" to a graphic range.

 

One centimeter is a reasonably small distance, so we more than likely do not want our bar range to have actually significant departments a lot smaller sized than this. A centimeter represents 14 kilometres, so a department of 10 km is most likely fine. As such we want to discover just how many kind of centimeters recurrent 10 km.

 

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In other words, we have the right to reexisting our 10 kilometres increment on the bar scale by measuring off 0.71 cm on the map. We"d draw the first tick at 0.71 cm, the second at 1.42 cm, and also so on:

 

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RF to Graphic Scale

This adds an added action to the example over. We have the right to find the map-distance equivalent of a ground distance, but we additionally need to be mindful around picking which ground distance we desire to portray on the map. Perhaps it"s most basic to pick a smaller ground distance that you have the right to then multiply to gain a reasonable bar scale.

 

(d) Convert an RF of 1:250,000 to a graphic scale

 

If we aren"t certain what increments a bar range would have actually for this scale, we might start out, say, via finding the map tantamount of 1 mile:

 

 

This can job-related fine, through one mile marked off on the map eextremely 0.25 inch; or, we might desire finer or broader increments, which we have the right to uncover by separating or multiplying the .25" as necessary.

RF to Verbal Scale

Aacquire we have to choose correct units to convert right into. Many verbal scales are either "one inch represents ____ miles," or "one centimeter represents ___ kilometers." These are reasonably easy to execute, because it implies only that we convert the denominator of our RF to the larger devices.

 

(e) Convert from RF of 1:25,000 to a verbal scale, in metric

 

Thus,

1 centimeter on this map represents 1/4 of a kilometer on the ground.

Graphic Scale to RF

Here we should take a measurement from the bar range to recognize the map distance that coincides to a ground distance.

 

(f) Find the RF range for the following graphic scale

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By measuring through a ruler, we discover that 10 kilometers actions 2.4 cm. We can usage this connection to uncover the RF for the bar scale:

 

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3. Determining Scale from a Map or Photo

Some maps may come via no range at all. Aerial photographs almost never execute (unmuch less one was painted on the ground before the photo was taken!). How deserve to you derive a range for use through the map or photo?

Actually the procedure is exceptionally equivalent to the last instance above. But instead of measuring along a bar scale, you have to meacertain the size of a things on the map or photo whose actual length you recognize. This could be a footsphere field, a city block, or the Equator (if it"s a civilization map). Often you can identify 1-mile-square sections in the US (watch the account below, under Survey Systems). You may also have to go out to the place mapped or pictured and measure the distance between two identifiable objects.

Once you have the two distances, you have the right to discover the range as over. For another instance, intend you have actually a map wright here the distance in between two section-line roads is 3.5 inches on the map. We can usually assume this is one mile on the ground (tright here are exceptions). The RF range is then:

 

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One caveat (exception) for air photos is that this approach assumes the two locations are at the very same elevation--or that the terrain is level. If you are utilizing air photos, the terrain may not be level. If tbelow are hills, also moderate ones, the calculations have the right to be thrvery own off. Keep this in mind for later on in the course.

Anvarious other way to calculate range on an unwell-known map or photo is to compare it to a map with a well-known range. For instance, suppose you have actually an air photo wbelow the distance in between two hills is 7.2 centimeters.You have a map of the exact same location at 1:24,000, and on the map the distance between the hills is 2.4 centimeters.

The answer involves a tiny algebra. Because the ground distance is the very same on both photo and map, we can create an expression for this ground distance for both, and then put them on either side of an equation. The ground distance can be uncovered by multiplying the map/photo distance by the scale (in this situation, by the inverse of the scale--notice how this provides the devices cancel correctly). We have to discover, for the photo, exactly how many kind of ground systems are stood for by one unit on the photo, so we use an x for this unknown quantity and also resolve for it:

 

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we have the right to cancel the units on each side and also divide by 7.2:

 

 

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In other words, the RF scale for the photo is 1:8,000.

 

4. Determining Distance and also Area from Map & Scale

Map scale isn"t much use in and of itself. We have the right to use a map"s range to recognize distances and locations on the map. Contrasted to converting in between scale types, calculating distance is simple. Area calculations are trickier, since we need to square the numbers.

Finding distance from map and also scale

As an instance, intend we have a map through a scale of 1:50,000. We meacertain the distance alengthy a property boundary as 1.7 cm. What is the size in the real world?

 

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To find ground distance, we need to use the map range to transform map distance to ground distance. Notice that aget we inverted the RF scale, so the devices will cancel appropriately. Once we multiply by the scale, we need to transform the ground distance to units suitable for ground measurement--in this situation, from centimeters to kilometers.

We can also calculate distance from verbal and graphic scales. With verbal scales, we use the same procedure as over through the RF. The just difference is that we need to use the units offered in the verbal scale (e.g., 1 inch to 17 miles). We"d more than likely desire to measure our map distance in the exact same systems (in this situation, inches) to make our convariation easy.

Graphic scales are probably the scales many generally provided by laypersons. You can note off a distance on the map and also compare it directly to the bar range. You need not know how many kind of inches or centimeters the map distance is. The main drawback of bar scales is that they are usually brief compared to the map itself, and therefore measuring longer ranges is hard.

Finding area measurement from map and scale

Area must be expressed in agenuine devices, which are generally distance units squared -- cm2 , mi2, and so on. We must therefore used squared convariation components when finding area from map dimensions.

For example, intend we measure a rectangular item of residential or commercial property that is 3 cm by 4 cm on a map. The map is at a range of 1:24,000. What is the location of the parcel?

The area of the parcel on the map is

 

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on the ground.

Because this is a huge number, we might desire to interpret to various other units. Tbelow are 10,000 square meters per hectare, so the area is 69 hectares (ha) (a hectare is about 2.5 acres). Or, tright here are (1,000)2 = 1,000,000 square meters per square kilometer, so the area is also 0.69 km2.

Notice that by composing the units as part of the problem, and also squaring them in addition to the numbers, our units cancel correctly and also we end up through a sensible answer.

There is another means to tackle area troubles if you have distance dimensions like 3 x 4 cm to start out the trouble. You have the right to transform the distance dimensions to real-people ranges first, and then multiply them to find the location. This provides the trouble longer however maybe easier.

B. Measurement Scales

1. Definition

Any type of indevelopment on a map (or in a table, a list, a survey, etc.) deserve to be explained in terms of just how pieces of the information can be related to each various other. Instances of mapped information include land-usage classes, road classes, city populations, and also county locations.

We can think of these kinds of indevelopment as either categorical (or qualitative) or numerical (or quantitative). Categorical information have the right to only be explained qualitatively, whereas items of numerical information have the right to be compared quantitatively. That is, numerical information is on a actual scale, such as distance (e.g., kilometers), location (e.g., hectares), or temperature (e.g., Celsius).

Example of categorical information:Land-Use categories of :1= forest, 2 = grassland, 3 = urban;We cannot say that based on the classes, 1 + 2 = 3 !We have the right to only usage the numbering to explain the items qualitatively.Example of Numerical indevelopment, city populations:Springarea = 100, Harmony = 200, Centerville = 300;We have the right to say that Centerville has actually as many type of human being as Springfield and also Harmony.

2. Four Measurement Levels

The categorical and also numerical types have actually traditionally been additionally damaged dvery own, each right into 2 levels of measurement:

Categorical indevelopment have the right to either be nominal level or ordinal level . At the nominal level, categories ssuggest explain different forms of points, and also cannot be compared to each other. Ordinal-level categories have the right to, on the other hand, be ranked against each other.

An instance of ordinal level would be road classes of interstate, major, secondary, and also primitive; although two major roads don"t make an interstate, you could say in a sense that interclaims are at a greater level than the others, at leastern in terms of cost to build!

The land-usage classes would certainly be an instance of nominal-level measurement. You most likely wouldn"t rank the classes against each other (unless you like one over the other, in which instance they could be ordinal!).

Numerical information deserve to either be interval level or proportion level . This distinction is subtle, and borders on synthetic. The only difference is that ratio-level indevelopment is on a scale that consists of a true zero, that is, a zero that truly represents a lack of whatever it is you"re measuring.

One of the few common examples of an interval range is temperature. You have the right to compare 2 temperature readings quantitatively. For example, 20 C is 15 levels warmer than 5 C. But the Celsius scale has actually an arbitrary zero suggest (the freezing temperature of water, or 32 F). 0 C doesn"t intend a absence of temperature. For this factor, 20 C is not four times as warm as 5 C! (One temperature range, Kelvin, does feature a true zero -- 0 K is -273 C, the temperature at which all molecular motion ceases). Fortunately, there are few examples of this on maps. You could want to incorporate an exception for elevation, which can be below sea level, or longitude, wright here the 0° line (Prime Meridian) is arbitrarily attracted on the globe.

 

 

Table 2: Measurement Levels

 

 

 

Measurement Level

Description

Examples

Categorical

Nominal

Simple categories; cannot rank categories

Colors; land also usage types; computer components

Categorical

Ordinal

Distinct categories; canrank categores in order

Road classes; flavor preferences

Numerical

Interval

Continuous scale; meacertain through numbers; realzero

Temperature; longitude, compass direction

Numerical

Ratio

Continuous scale; measurevia numbers; genuine zero

Distance; weight; financial institution balance

Most numerical scales are ratio-level. We have the right to compare 20 kilometres via 10 kilometres in any number of ways, including saying the first is twice as much as the second.

3. So What?

We will usage this terminology frequently to describe the kinds of information on maps and also in other resources. You will also encounter it somewhere else, I guarantee it!

Indevelopment often is analyzed from one level to an additional. The basic preeminence is that it"s easier to translate to a reduced level (e.g., from ratio to ordinal) than to a higher level. In most instances, it"s impossible to go legitimately to a higher level. Why bvarious other making use of a lower-level scale? Often it conserves space and power to usage a reduced scale.

For example, if you have actually a table of city populations in Sonoma County (i.e., ratio level) and also want to present population on a map, you can print a number alongside each city name. This would preserve your ratio-level data on the map itself. An even more prevalent approach is to have actually a collection of significantly big signs for the city place, each symbol indicating a variety of population. These icons would certainly offer ordinal-level information around populace. This conveniently reduces the clutter on the map, however you cannot recover the original ratio-level numbers from the map.

C. Accuracy, Precision, and also Significant Digits

1. Accuracy versus Precision

Some people make a distinction between accuracy and precision.

Accuracy would certainly be exactly how close a measured value is to the actual value.

Precision would be the number of digits reported through the worth. For instance, I included a thermometer to my automobile that shows the exterior temperature to tenths of a degree (e.g., 65.2° F). The thermometer"s precision is to tenths of a level Fahrenheit. But it regularly seems to provide readings that are also high, probably because of the engine"s warmth nearby. Its accuracy, then, could just be to within 5° F.

2. Huge Digits

Huge digits are the variety of digits in a worth that have actually genuine meaning and reflect the accuracy of the worth or measurement. For example, a distance measurement of 45.8 km would have three substantial digits. The value means that the measurement was made to an accuracy of tenths of a kilometer. If the instrument, such as an odometer, is not precise, the value should not encompass as many type of considerable digits. Of course, if the instrument procedures even more accurately than this, the value should be reported through the proper precision.

The major suggest is to beware dimensions via very specific worths as soon as the accuracy could be called right into question. This is particularly true once converting values from one type of range to one more. For instance, if I measure a map distance as 11 inches with an plain ruler, then desire to convert to centimeters, I discover on my calculator:

 

(11 in.) * (2.54 cm/in.) = 27.94 cm

 

But 27.94 cm means high accuracy, which I didn"t have actually with the original measurement. The solution right here is to round the answer to about the very same variety of significant digits as the original measurement. In this case, I have to probably say the distance is 28 cm.

More example of considerable digits:

Two substantial digits: 3700, 37, 3.7, 0.37, 0.0037Four significant digits: 19120, 19.12, 0.001912, 19.00, 0.1900

Notice that zeroes added after the decimal suggest suggest precision equal to any other digits. Typically, zeroes to the best of other digits (e.g., 3700) are not considered substantial, unless a decimal allude is included and more zeroes occur to the best of it (e.g., 3700.0 suggests 5 substantial digits). What if we have a measurement of 1900 wright here the zeroes are significant? Traditionally, a bar is inserted over the zeroes to suggest definition.

Another solution is to usage scientific notation.

For example, 3700 through the zeroes actually being substantial have the right to be written as 3.700 x 103. This breaks the number dvery own into the mantissa (the substantial digits, right here 3.700) and the exponent on the ten (below 3). In clinical notation, only one digit is inserted before the decimal suggest in the mantissa. The exponent on the 10 shows how many type of locations the decimal point have to be relocated to reclaim the number to plain notation (in this situation, 3 places to the right; this is tantamount to multiplying the mantissa by 1000). Negative exponents suppose smaller sized numbers, and we change the decimal allude to the left. For instance, 3.700 x 10-4 is the same as 0.0003700. Scientific notation is handy via incredibly big or little numbers. Numbers in scientific notation have the right to be supplied simply prefer other numbers, as lengthy as you follow the rules of exponents -- for multiplying, dividing, and so on.

D. Category, Simplification and also Symbolization of Data

This is not a course in cartography, so we will certainly not deal in information via just how data is classified and streamlined for mapping, and exactly how symbols are created to suit those data. But you have to be mindful that any kind of map, consisting of topographic maps, is the outcome of most handling of the data behind the map. Here is a brief discussion of some elements that go right into information processing for maps.

1. Classification

Maps must take the pertinent data and assign it to a given variety of classes, each via its own number of members. Instances are maps of land supplies and also of temperature. For categorical data prefer land supplies, it is basic to overfill the map reader through too many kind of classes. Cartographers recommend a maximum of five or six various classes (for land use, these might be forest, rangeland also, cropland, water, and also urban). Numerical data presented on isarithmic maps (which show areas of equal values) have the right to be somewhat even more facility. For example, temperature areas have the right to trfinish from 80"s F to -20"s F. But the information need to be displayed through logical symbolization (see below).

Documents deserve to be damaged down into categories in 3 ways:

(a) Each category have the right to have actually an equal variety of members. For instance, in a map of US population by state, we could have five categories of populace, each via ten says.

(b) Each category can span an equal interval of values. In the populace map, we would certainly take the range of populaces (highest possible state minus lowest state), and also divide the range by five. Each category would be one-fifth of the overall selection. In this map, categories may have actually different numbers of claims. The greatest category might just have actually a couple of states (e.g., The golden state, New York and also Texas), and also other categories may have a huge number of states.

(c) Finally, we can subjectively assign says to classes, maybe by in search of "natural breaks" in populace ranmonarchs. Often map-machines begin out through one of the initially 2 methods, then refine it by looking at the outcomes and also transforming classes slightly. All of this should reflect the purposes of the map. Different methods have the right to develop radically different-looking maps (view any type of cartography text for examples).

2. Simplification

A second major task in map-making is simplifying the information behind the map. Group is one method of simplifying the data we usage going right into the map. Often this involves lowering the measurement level of the information (such as transdeveloping ratio-level data to ordinal-level data, as in our example of city populations suggested by assorted circle sizes).

Another simplification job relates to the spatial aspects of the data. For instance, mountainous roadways might take many twists and also turns. A map that reflects all these curves would certainly be cluttered and messy. We might desire to generalize the road spatially to clarify things. Beware, of course, those map users that curse you for those curves they didn"t expect! The cartographer"s project is to simplify without distorting and misleading the map user.

Sometimes the job might necessitate eliminating functions altogether. For instance, a small-scale US map deserve to display only schosen cities; just how do you select which cities to include without offending also many people? I observed a US map recently that included moderate-sized cities however omitted my hometvery own, San Diego (now the sixth biggest city in the US).

3. Symbolization

Symbolization of information is an additional vital part of interacting through maps. What symbols are preferred will affect whether will people will certainly understand, or also usage, a map. Symbols should be chosen so that the intfinished audience will understand also them. Different icons have to be used for general-purpose maps than those intfinished for professionals in a area.

Symbols deserve to be inserted on a continuum in between intuitive and abstract. Intuitive icons imply to the reader what they recurrent. Pictographs are recognizable representations of the actual objects. For instance, marshes are frequently presented via swampy grass symbols, or airports as planes. On the various other excessive are abstract icons via no noticeable link to what they recurrent. Examples are circles as cities, or streams as dotted lines. Some abstract icons have actually been used so commonly to represent a particular function that, although abstract, they execute attach through the object in a lot of people"s minds. A star within a circle, for circumstances, generally suggests a resources city.

Symbols deserve to additionally be classed according to their dimension: point (0-dimension), line (1-dimension) or area (2-dimension) signs. Like the various other 2, allude icons can convey categorical or numerical indevelopment. Instances of categorical suggest icons are airports, campgrounds, springs, and also quarries. Variable-sized circles for city population would be examples of numerical suggest icons.

 

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Line signs deserve to convey indevelopment about linear features, such as roads, railroadways, and also streams. Another vital use of lines on maps are isolines. Isolines (likewise referred to as isarithms) connect points of equal worth. You"ll frequently check out these on a map of temperatures on the weather page of the newspaper. Eexceptionally location alengthy an isoline on this map has the very same temperature, at leastern theoretically. This indicates additionally that areas between 2 isolines have actually worths somewbelow in between the worths of the surrounding lines. Without extra indevelopment, we cannot say through confidence a lot even more around intervening values. We deserve to estimate, or interpolate, the intervening values, for example by measuring the distance of a suggest from each line. Tright here is no guarantee, of course, that our estimate is really correct, so beware such estimates from isoline maps.

 

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An necessary kind of isoline for this course is the elevation contour . These isolines show equal elevations, and also are included on all USGS topographic maps. The contour interval is the height distinction in between each contour. Contour intervals on USGS maps differ depending on the terrain. Typical intervals on 1:24,000-range maps are 20, 40 and 80 feet. A 20-foot interval would display, for instance, contours at 0 (sea level), 20, 40, 60, 80, and so on.

It takes some practice to feel comfortable working through elevation contours and other isoline maps. We will certainly have actually lab exercises to give you some practice through them, including visualizing terrain and constructing prodocuments, or two-dimensional views of just how elevation changes on a line throughout the topographic map.

The areas in between isolines are frequently shaded or colored to portray the information more properly. Temperature maps in a lot of newsfiles are now in shade, with warmer areas acquiring "warmer" colors, colder areas "cooler" colors. These shaded-isoline areas are a blend of line and also area icons.

Speaking of color and also shading, let us cover one last allude around map symbolization. The rules around using color and shading are different for nominal versus higher-level data (ordinal, interval, and also ratio). If you are mapping nominal-level data, the categories have actually no certain order, and also you most likely want to maximize the contrast between categories. Land offers, for example, must be shown so that you deserve to separate urban, subcity, forest, and also pasture, or whatever categories you include on the map.

Ordinal, interval or proportion data have to be mapped differently. Here there is a definite ordering of categories. To usage the temperature map again, we have a trend from heat to cold in the areas we portray. We want the map reader to immediately appreciate this gradual trend in the information. Therefore we select an ordering of colors or signs that conveys this constant trend in the information, for example: red-orange-yellow-green-blue-violet.

See more: After The Fact The Art Of Historical Detection Chapter Summaries

Many kind of civilization make the mistake of reasoning they must pick colors that maximize contrast in between categories, even through ordinal or higher-level data. Beware this mistake! You may be able to pick out categories easily with this strategy, yet you ruin the impression of a trend in the information.