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A. Map Scale

B. Measure Scales

C. Accuracy, Precision, and far-reaching Digits

D. Classification, Simplification and Symbolization of Data

A. Map range

Map range is the relationship in between a unit of length on a map and the matching length top top the ground. We will certainly use concepts of map scale throughout the course, for this reason it will certainly pay girlfriend to examine this ar carefully.

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1. Types of Map Scales

We deserve to relate map and also ground with 3 different species of scale. Verbal scale expresses in native a relationship in between a map distance and a ground distance. Typically it is along the lines of:


One inch represents 16 miles.


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

The second kind of scale is a graphic scale, or bar scale. This shows straight on the map the equivalent ground distance. Because that example:




The third form of range is a representative fraction, or proportion scale. Contrasted to the very first two, it is the most abstract, but also the most versatile. A representative fraction, or RF, shows the relationship between one of any type of unit on the map and one that the exact same unit top top the ground. RFs may be shown as an yes, really fraction, for example 1/24,000, but are typically written through a colon, together in 1:24,000. In this example, one unit of any length (one mm, one cm, one inch, one foot, etc.) ~ above the map represents 24,000 the those exact same units top top the soil (24,000 mm, 24,000 cm, 24,000", 24,000", etc.). The RF is versatile due to the fact that you room not tied to any certain units. You may work in any type of unit friend choose, one of two people metric, English, or other.

The RF is a called a portion because that is simply that--a fraction that shows how much the real human being is diminished to right on the map. A great comparison is regularly made with scale models that automobiles or aircraft. A 1/32-model of an auto is 1/32nd as huge as the actual auto. In the same way, a 1:100,000-scale map is 1/100,000th as big as the floor area shown on the map.

A connected idea is that of little scale versus large scale. Geographers use these terms in different way than numerous people. A large scale map is wherein the RF is relatively large. A 1:1200 map is as such larger range than a 1:1,000,000 map. The 1:1,000,000 map would commonly be called a small scale map. This is true even though the 1:1,000,000 map would present a much larger area than the 1:1200 map.

Here is a ascendancy of thumb for dimension of scale by RF:



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


Of course, what is small or big scale is relative. Ns noticed a surveying text (Brinker & Wolf, 1984) that classed anything smaller than 1:12,000 as small scale -- surveyors rarely occupational with anything smaller sized than this.

The large/small scale terminology can end up being confusing once talking about big versus little areas. If you space talking about a phenomenon that occurs throughout a huge region, the is tempting to say it"s a large phenomenon (e.g., "the woodland blight is a large disease"). But due to the fact that the map the would show this would certainly be small-scale, that is far better to use a various term to avoid confusion. My favourite is "broad-scale."

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

2. Converting in between Scale Types

If girlfriend are given one form of scale, girlfriend should be able to derive or construct any type of of the various other two. This takes some practice, and some troubles are included in your lab exercises. Some instances are offered below.

A crucial step in doing any kind of counter that requires differing units is to incorporate the units in the difficulty itself. You deserve to then cancel the devices by multiply or dividing. This method you avoid ending up being confused about which conversion components to use and also how to use them.

Verbal range to RF

The an essential here is to write the verbal range as a fraction, then convert so the both numerator and denominator have the same units, and the numerator has a 1.


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





or 1:1,140,000.

Notice the the resulting fraction is rounded so that the RF does no imply more accuracy 보다 the initial precision warranted.


(b) transform verbal scale of "15 centimeter to 1 km" to RF




or 1:6700.

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

For example, in (a) above, we might have supplied the truth that 1 mile = 63,360 inches come skip a step.

Verbal scale to graphic Scale

Usually this is a relatively easy job if the map offers us reasonable units in the linguistic scale. We can use the linguistic scale choose a fraction to transform the ground street to map distance.


(c) transform verbal range of "1 centimeter to 14 km" come a graphics scale.


One centimeter is a fairly small distance, for this reason we probably don"t want our bar range to have major divisions lot smaller than this. A centimeter represents 14 km, so a department of 10 km is probably fine. Therefore we want to discover how countless centimeters stand for 10 km.




In other words, we deserve to represent ours 10 kilometres increment ~ above the bar range by measuring turn off 0.71 centimeter on the map. We"d attract the very first tick at 0.71 cm, the 2nd at 1.42 cm, and also so on:




RF to Graphic Scale

This add to an extra step to the instance above. Us can uncover the map-distance identical of a floor distance, however we also need to be careful around choosing i beg your pardon ground street we want to portray ~ above the map. Possibly it"s simplest to pick a smaller sized ground distance that you can then main point to obtain a reasonable bar scale.


(d) convert an RF that 1:250,000 to a graphics scale


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



This might work fine, through one mile significant off on the map every 0.25 inch; or, we might want finer or wider increments, which us can discover by splitting or multiply the .25" as needed.

RF to verbal Scale

Again we have to choose ideal units to convert into. Most verbal scales room either "one inch represents ____ miles," or "one centimeter to represent ___ kilometers." this are fairly easy to do, due to the fact that it means only the we convert the denominator of ours RF come the bigger units.


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



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

Graphic scale to RF

Here we need to take a measurement native the bar range to recognize the map street that coincides to a soil distance.


(f) uncover the RF range for the adhering to graphic scale



By measuring through a ruler, we discover that 10 kilometers actions 2.4 cm. We deserve to use this partnership to find the RF for the bar scale:




3. Determining scale from a Map or Photo

Some maps might come through no range at all. Aerial photographs practically never carry out (unless one to be painted top top the ground prior to the photo was taken!). How can you derive a scale for use v the map or photo?

Actually the procedure is very similar to the last instance above. But instead that measuring along a bar scale, you have to measure the length of things on the map or photo whose actual size you know. This can be a football field, a city block, or the Equator (if it"s a people map). Often you deserve to identify 1-mile-square part in the united state (see the account below, under survey Systems). Girlfriend may even need to go the end to the ar mapped or pictured and also measure the distance between two identifiable objects.

Once you have the two distances, girlfriend can discover the range as above. For another example, suppose you have actually a map wherein the distance in between two section-line roadways is 3.5 inch on the map. We can usually assume this is one mile ~ above the floor (there are exceptions). The RF range is then:




One caveat (exception) for air photos is that this technique assumes the two areas are at the exact same elevation--or the the terrain is flat. If you room using wait photos, the terrain may not be flat. If there room hills, also moderate ones, the calculations deserve to be thrown off. Store this in psychic for later on in the course.

Another method to calculate scale on one unknown map or photograph is to compare it come a map with a recognized scale. For example, intend you have an air picture where the distance in between two hills is 7.2 centimeters.You have actually a map that the same area in ~ 1:24,000, and on the map the distance between the hills is 2.4 centimeters.

The answer requires a tiny algebra. Because the ground distance is the same on both photo and also map, we can create an expression because that this ground distance for both, and also then put them on either next of one equation. The floor distance can be uncovered by multiplying the map/photo street by the range (in this case, through the inverse of the scale--notice just how this renders the units cancel correctly). We need to find, because that the photo, how numerous ground devices are stood for by one unit ~ above the photo, for this reason we use an x for this unknown quantity and solve for it:








we can cancel the devices on each side and divide by 7.2:






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


4. Determining Distance and also Area indigenous Map & Scale

Map scale isn"t much use in and also of itself. We can use a map"s range to recognize distances and areas on the map. Contrasted to converting in between scale types, calculating distance is simple. Area calculations are trickier, due to the fact that we need to square the numbers.

Finding street from map and scale

As an example, mean we have actually a map with a scale of 1:50,000. We measure the distance along a property boundary together 1.7 cm. What is the size in the real world?




To find ground distance, we must use the map range to convert map distance to ground distance. An alert that again us inverted the RF scale, for this reason the units will cancel properly. As soon as we main point by the scale, we require to transform the ground street to units suitable for floor measurement--in this case, native centimeters to kilometers.

We can additionally calculate distance from verbal and graphic scales. Through verbal scales, we usage the very same procedure as over with the RF. The only distinction is the we need to use the units offered in the verbal range (e.g., 1 customs to 17 miles). We"d more than likely want to measure up our map distance in the very same units (in this case, inches) to make our counter easy.

Graphic scale are most likely the scale most frequently used by laypersons. You deserve to mark turn off a distance on the map and also compare it directly to the bar scale. You need not recognize how many inches or centimeters the map street is. The main drawback the bar scales is that they space usually brief compared to the map itself, and also hence measuring longer distances is difficult.

Finding area measurement native map and also scale

Area have to be to express in areal units, which space usually distance systems squared -- cm2 , mi2, and so on. Us must because of this used squared conversion factors when finding area indigenous map measurements.

For example, mean we measure up a rectangular piece of home that is 3 cm by 4 centimeter on a map. The map is at a scale of 1:24,000. What is the area the the parcel?

The area that the parcel on the map is










on the ground.

Since this is a huge number, we could want to interpret to other units. There are 10,000 square meters every hectare, so the area is 69 hectares (ha) (a hectare is around 2.5 acres). Or, there space (1,000)2 = 1,000,000 square meters per square kilometer, for this reason the area is additionally 0.69 km2.

Notice that by composing the systems as part of the problem, and squaring them in addition to the numbers, our systems cancel properly and we finish up v a sensible answer.

There is another way to tackle area problems if you have distance dimensions prefer 3 x 4 cm to start out the problem. Girlfriend can transform the distance dimensions come real-world ranges first, and also then multiply them to uncover the area. This renders the difficulty longer yet perhaps simpler.

B. Measurement scale

1. Definition

Any kind of details on a map (or in a table, a list, a survey, etc.) have the right to be defined in terms of just how pieces of the information deserve to be related to each other. Examples of mapped information incorporate land-use classes, road classes, city populations, and also county areas.

We deserve to think that these types of information as either categorical (or qualitative) or number (or quantitative). Categorical information deserve to only be described qualitatively, whereas items of number information have the right to be contrasted quantitatively. That is, numerical details is ~ above a actual scale, together as street (e.g., kilometers), area (e.g., hectares), or temperature (e.g., Celsius).

Example that categorical information:Land-Use category of :1= forest, 2 = grassland, 3 = urban;We can not say that based on the classes, 1 + 2 = 3 !We have the right to only usage the number is numbered to define the items qualitatively.Example of number information, city populations:Springfield = 100, Harmony = 200, Centerville = 300;We deserve to say the Centerville has as many civilization as Springfield and Harmony.

2. Four Measurement Levels

The categorical and numerical types have traditionally to be further damaged down, each into two level of measurement:

Categorical information can either be nominal level or ordinal level . At the nominal level, categories simply define different species of things, and also cannot be contrasted to each other. Ordinal-level category can, on the various other hand, be ranked against each other.

An instance of ordinal level would be roadway classes that interstate, primary, secondary, and also primitive; back two main roads don"t do an interstate, you might say in a feeling that interstates space at a greater level 보다 the others, at least in terms of expense to build!

The land-use classes would certainly be an instance of nominal-level measurement. You more than likely wouldn"t location the classes versus each various other (unless you favor one over the other, in which case they could be ordinal!).

Numerical information deserve to either it is in interval level or proportion level . This distinction is subtle, and also borders on artificial. The only distinction is the ratio-level info is ~ above a scale that contains a true zero, that is, a zero that truly represents a absence of every little thing it is you"re measuring.

One that the few common instances of an interval scale is temperature. You have the right to compare two temperature readings quantitatively. For example, 20 C is 15 degrees warmer 보다 5 C. However the Celsius scale has actually an arbitrarily zero point (the freezing temperature that water, or 32 F). 0 C doesn"t average a absence of temperature. For this reason, 20 C is not 4 times as heat as 5 C! (One temperature scale, Kelvin, does function a true zero -- 0 K is -273 C, the temperature at which every molecular motion ceases). Fortunately, there are few examples the this ~ above maps. You might want to include an exception for elevation, which can be listed below sea level, or longitude, whereby the 0° heat (Prime Meridian) is arbitrarily attracted on the globe.



Table 2: measure Levels




Measurement Level





Simple categories; can not rank categories

Colors; land usage types; computer components



Distinct categories; canrank categores in order

Road classes; odor preferences



Continuous scale; measure v numbers; realzero

Temperature; longitude, compass direction



Continuous scale; measurewith numbers; genuine zero

Distance; weight; bank balance

Most numerical scales room ratio-level. We can compare 20 kilometres with 10 kilometres in any variety of ways, consisting of saying the an initial is twice as much as the second.

3. So What?

We will usage this terminology commonly to explain the kinds of information on maps and in other sources. You will additionally encounter it elsewhere, ns guarantee it!

Information frequently is translated from one level to another. The general dominance is that it"s much easier to analyze to a lower level (e.g., from ratio to ordinal) 보다 to a greater level. In many cases, it"s impossible to walk legitimately to a greater level. Why bother using a lower-level scale? often it saves space and energy to use a reduced scale.

For example, if you have actually a table that city populaces in Sonoma county (i.e., proportion level) and want to show population on a map, you could print a number alongside each city name. This would preserve your ratio-level data top top the map itself. A an ext common technique is to have a collection of increasingly large symbols for the city location, every symbol describe a range of population. These signs would give ordinal-level information about population. This conveniently reduce the clutter top top the map, but you cannot recoup the initial ratio-level numbers from the map.

C. Accuracy, Precision, and far-reaching Digits

1. Accuracy versus Precision

Some human being make a distinction between accuracy and also precision.

Accuracy would be exactly how close a measured value is come the yes, really value.

Precision would certainly be the number of digits reported v the value. Because that example, I added a thermometer to my car that reflects the exterior temperature to one per 10 of a degree (e.g., 65.2° F). The thermometer"s precision is to one per 10 of a degree Fahrenheit. Yet it often seems to give readings that are too high, perhaps due to the engine"s warm nearby. That accuracy, then, could only be to in ~ 5° F.

2. Far-ranging Digits

Significant digits room the variety of digits in a worth that have actually real meaning and reflect the accuracy that the worth or measurement. For example, a distance measurement the 45.8 kilometres would have actually three far-reaching digits. The value means that the measurement was made to an accuracy of one per 10 of a kilometer. If the instrument, such together an odometer, is no accurate, the value need to not encompass as many significant digits. Of course, if the tool measures much more accurately than this, the value should be reported v the ideal precision.

The main suggest is to beware measurements with highly an accurate values when the accuracy might be referred to as into question. This is particularly true when converting worths from one sort of range to another. For example, if ns measure a map street as 11 inches v an ordinary 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 suggests high accuracy, which ns didn"t have with the original measurement. The solution right here is to round the price to around the same number of far-ranging digits together the original measurement. In this case, i should more than likely say the street is 28 cm.

More instance of significant digits:

Two far-reaching digits: 3700, 37, 3.7, 0.37, 0.0037Four far-reaching digits: 19120, 19.12, 0.001912, 19.00, 0.1900

Notice that zeroes included after the decimal point imply precision same to any other digits. Normally, zeroes come the ideal of various other digits (e.g., 3700) space not taken into consideration significant, unless a decimal point is included and an ext zeroes take place to the ideal of the (e.g., 3700.0 means 5 far-ranging digits). What if we have actually a measurement of 1900 where the zeroes are significant? Traditionally, a bar is inserted over the zeroes to show significance.

Another systems is come use scientific notation.

For example, 3700 v the zeroes in reality being significant can be composed as 3.700 x 103. This breaks the number down right into the mantissa (the significant digits, right here 3.700) and also the exponent on the ten (here 3). In scientific notation, just one digit is placed prior to the decimal point in the mantissa. The exponent top top the 10 suggests how plenty of places the decimal point should be relocated to regain the number to simple notation (in this case, three areas to the right; this is identical to multiplying the mantissa by 1000). Negative exponents mean smaller numbers, and also we change the decimal point to the left. For example, 3.700 x 10-4 is the very same as 0.0003700. Scientific notation is handy v very large or little numbers. Number in scientific notation deserve to be used similar to other numbers, as long as you follow the rule of exponents -- because that multiplying, dividing, etc.

D. Classification, Simplification and Symbolization of Data

This is not a food in cartography, so we will not deal in detail with exactly how data is classified and also simplified for mapping, and how signs are produced to fit those data. Yet you need to be aware that any kind of map, including topographic maps, is the result of a most processing of the data behind the map. Below is a quick discussion the some facets that get in data processing for maps.

1. Classification

Maps need to take the relevant data and assign it come a given number of classes, each through its own variety of members. Instances are maps of floor uses and of temperature. Because that categorical data favor land uses, that is easy to overload the map reader v too countless classes. Cartographers introduce a maximum of five or six various classes (for floor use, these can be forest, rangeland, cropland, water, and also urban). Numerical data displayed on isarithmic maps (which display zones of same values) have the right to be somewhat much more complex. Because that example, temperature zones deserve to trend from 80"s F come -20"s F. Yet the data should be shown with reasonable symbolization (see below).

Data can be broken down right into categories in three ways:

(a) Each classification can have actually an equal variety of members. Because that example, in a map that US population by state, we could have five categories the population, each with ten states.

(b) Each group could span an same interval the values. In the populace map, we would take the range of populaces (highest state minus shortest state), and divide the variety by five. Each group would it is in one-fifth of the all at once range. In this map, categories may have various numbers of states. The highest classification may only have actually a few states (e.g., California, new York and Texas), and also other category may have a large number that states.

(c) Finally, we might subjectively assign claims to classes, possibly by looking for "natural breaks" in populace rankings. Often map-makers start out with among the first two methods, climate refine that by looking at the results and changing classes slightly. All of this should reflect the purposes of the map. Various methods can produce radically different-looking maps (see any type of cartography text for examples).

2. Simplification

A second significant task in map-making is simplifying the info behind the map. Group is one means of simplifying the data we use going into the map. Regularly this entails lowering the measure up level of the data (such as transforming ratio-level data to ordinal-level data, together in our instance of city populations shown by miscellaneous circle sizes).

Another simplification job relates come the spatial facets of the data. Because that example, like the mountain roads might take plenty of twists and also turns. A map that reflects all these curves would be cluttered and messy. We might want come generalize the roadway spatially come clarify things. Beware, of course, those map customers who curse you because that those curve they didn"t expect! The cartographer"s job is to leveling without distorting and misleading the map user.

Sometimes the task may necessitate eliminating attributes altogether. For example, a small-scale united state map can present only selected cities; how do you pick which cities to incorporate without offending too numerous people? I observed a us map newly that had moderate-sized cities but omitted my hometown, mountain Diego (now the 6th largest city in the US).

3. Symbolization

Symbolization of info is another an important part of interacting through maps. What symbols are liked will influence whether will world will understand, or even use, a map. Symbols need to be chosen so that the plan audience will understand them. Different symbols should be used for general-purpose maps than those to plan for specialists in a field.

Symbols can be inserted on a continuum between intuitive and also abstract. Intuitive symbols imply to the leader what lock represent. Pictographs are recognizable representations of the yes, really objects. Because that example, marshes space often displayed with swampy grass symbols, or airports as planes. ~ above the other too much are abstract symbols with no apparent connection come what they represent. Examples are circles together cities, or streams together dotted lines. Some abstract symbols have actually been offered so extensively to represent a details feature that, return abstract, they do attach with the object in most people"s minds. A star in ~ a circle, for instance, usually means a resources city.

Symbols can additionally be classed according to your dimension: suggest (0-dimension), heat (1-dimension) or area (2-dimension) symbols. Choose the various other two, suggest symbols have the right to convey categorical or numerical information. Instances of categorical suggest symbols room airports, campgrounds, springs, and also quarries. Variable-sized circles because that city populace would be instances of numerical point symbols.




Line symbols can convey information around linear features, such as roads, railroads, and streams. An additional important use of currently on maps space isolines. Isolines (also called isarithms) connect points of equal value. You"ll regularly see this on a map of temperatures on the weather web page of the newspaper. Every ar along one isoline ~ above this map has the same temperature, at the very least theoretically. This implies likewise that places between two isolines have actually values somewhere between the values of the bordering lines. Without extr information, we cannot say through confidence much an ext about intervening values. We have the right to estimate, or interpolate, the intervening values, for example by measure up the distance of a suggest from each line. Over there is no guarantee, of course, the our calculation is yes, really correct, so beware such approximates from isoline maps.




An important type of isoline because that this course is the elevation contour . This isolines show equal elevations, and also are consisted of on every USGS topographic maps. The edge interval is the elevation difference in between each contour. Contour intervals top top USGS maps vary depending on the terrain. Usual intervals ~ above 1:24,000-scale maps room 20, 40 and 80 feet. A 20-foot interval would certainly show, because that example, border at 0 (sea level), 20, 40, 60, 80, and so on.

It take away some exercise to feeling comfortable working through elevation contours and other isoline maps. Us will have lab practice to provide you some exercise with them, including visualizing terrain and also constructing profiles, or two-dimensional see of how elevation changes on a line throughout the topographic map.

The zones in between isolines are often shaded or colored to portray the information much more effectively. Temperature maps in most newspapers are currently in color, through warmer zones obtaining "warmer" colors, colder locations "cooler" colors. This shaded-isoline zones room a mix of line and also area symbols.

Speaking that color and also shading, let us cover one final point around map symbolization. The rules around using color and also shading are different for nominal versus higher-level data (ordinal, interval, and ratio). If you are mapping nominal-level data, the categories have no details order, and you probably want to maximize the contrast between categories. Soil uses, for example, need to be portrayed so the you have the right to separate urban, suburban, forest, and pasture, or whatever categories you encompass on the map.

Ordinal, interval or ratio data need to be mapped differently. Here there is a definite ordering of categories. To usage the temperature map again, we have actually a trend from warm to cold in the zones we portray. We want the map reader to instantly appreciate this gradual trend in the data. Thus we choose an ordering of color or signs that conveys this constant trend in the data, because that example: red-orange-yellow-green-blue-violet.

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Many civilization make the mistake of reasoning they should pick colors that maximize contrast between categories, also with ordinal or higher-level data. Beware this mistake! friend may be able to pick the end categories quickly with this approach, yet you damage the impression the a trend in the data.