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A. Map Scale

B. Measurement Scales

C. Accuracy, Precision, and far-reaching Digits

D. Classification, Simplification and also Symbolization of Data

## A. Map range

Map range is the relationship between a unit of size on a map and also the matching length ~ above the ground. We will certainly use principles of map scale throughout the course, so it will certainly pay friend to examine this section carefully.

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

### 1. Varieties of Map Scales

We deserve to relate map and also ground with three different species of scale. Verbal scale expresses in words a relationship in between a map distance and a floor distance. Generally it is along the lines of:

One customs represents 16 miles.

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

The second type of scale is a graphics scale, or bar scale. This shows directly on the map the corresponding ground distance. For example: The third type of scale is a representative fraction, or ratio scale. Compared to the an initial two, that is the many abstract, but also the many versatile. A representative fraction, or RF, mirrors the relationship in between one of any unit ~ above the map and also one the the exact same unit ~ above the ground. RFs might be presented as an yes, really fraction, for example 1/24,000, but are generally written v a colon, together in 1:24,000. In this example, one unit of any type of length (one mm, one cm, one inch, one foot, etc.) top top the map to represent 24,000 that those exact same units top top the floor (24,000 mm, 24,000 cm, 24,000", 24,000", etc.). The RF is versatile since you space not tied to any certain units. You may work in any unit girlfriend choose, one of two people metric, English, or other.

The RF is a dubbed a portion because that is simply that--a portion that shows how much the real human being is lessened to right on the map. A good comparison is frequently made with scale models that automobiles or aircraft. A 1/32-model of one auto is 1/32nd as large as the yes, really auto. In the exact same way, a 1:100,000-scale map is 1/100,000th as big as the soil area presented on the map.

A related idea is the of tiny scale versus big scale. Geographers use these terms in different way than countless people. A big scale map is whereby the RF is reasonably large. A 1:1200 map is because of this larger scale than a 1:1,000,000 map. The 1:1,000,000 map would normally be called a tiny scale map. This is true even though the 1:1,000,000 map would display a much larger area 보다 the 1:1200 map.

Here is a dominion of ignorance for size of range 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 tiny or large scale is relative. I noticed a surveying message (Brinker & Wolf, 1984) that classed anything smaller than 1:12,000 as small scale -- surveyors rarely occupational with anything smaller than this.

The large/small range terminology can end up being confusing once talking about huge versus tiny areas. If you space talking about a phenomenon that occurs throughout a big region, that is tempting come say it"s a massive phenomenon (e.g., "the forest blight is a large-scale disease"). But because the map that would present this would certainly be small-scale, it is better to usage a different term to avoid confusion. My favorite is "broad-scale."

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

### 2. Converting between Scale Types

If you are provided one type of scale, girlfriend should be able to derive or construct any type of of the other two. This takes some practice, and also some troubles are included in her lab exercises. Some examples are provided below.

A crucial step in doing any type of kind of conversion that involves differing systems is to incorporate the devices in the difficulty itself. You deserve to then release the systems by multiplying or dividing. This means you avoid becoming confused around which conversion factors to use and also how to usage them.

Verbal scale to RF

The key here is to create the verbal range as a fraction, then transform so that both numerator and denominator have actually the exact same units, and also the numerator has a 1.

(a) convert verbal range of "1" come 18 miles" come RF or 1:1,140,000.

Notice that the resulting portion is rounded so that the RF does not imply much more accuracy than the initial precision warranted.

(b) convert verbal range of "15 centimeter to 1 km" come RF or 1:6700.

In many conversions you can save steps if girlfriend remember extr equivalencies.

For example, in (a) above, we can have offered the fact that 1 mile = 63,360 inches to skip a step.

Verbal range to graphic Scale

Usually this is a reasonably easy job if the map provides us reasonable units in the verbal scale. We have the right to use the linguistic scale prefer a portion to change the ground distance to map distance.

(c) transform verbal scale of "1 cm to 14 km" to a graphics scale.

One centimeter is a fairly small distance, for this reason we most likely don"t want our bar range to have major divisions lot smaller 보다 this. A centimeter to represent 14 km, for this reason a division of 10 km is most likely fine. As such we desire to find how plenty of centimeters represent 10 km. In various other words, we deserve to represent our 10 km increment on the bar range by measuring turn off 0.71 cm on the map. We"d draw the first tick in ~ 0.71 cm, the second at 1.42 cm, and also so on: RF to Graphic Scale

This to add an extra step to the instance above. We can uncover the map-distance equivalent of a ground distance, but we also need to it is in careful about choosing i beg your pardon ground distance we want to portray ~ above the map. Probably it"s simplest to pick a smaller ground street that you have the right to then main point to get a reasonable bar scale.

(d) convert an RF the 1:250,000 come a graphic scale

If we aren"t sure what increments a bar scale would have for this scale, we can start out, say, v finding the map identical of 1 mile:

This might work fine, with one mile significant off top top the map every 0.25 inch; or, we might want finer or wider increments, which us can uncover by dividing or multiply the .25" as needed.

RF to linguistic Scale

Again we have to choose ideal units to convert into. Many verbal scales are either "one inch represents ____ miles," or "one centimeter to represent ___ kilometers." these are reasonably easy to do, because it way only the we convert the denominator of our RF come the larger units.

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

Therefore,

1 centimeter on this map to represent 1/4 the a kilometre on the ground.

Graphic scale to RF

Here we should take a measurement from the bar scale to determine the map distance that corresponds to a ground distance.

(f) find the RF scale for the following graphic scale By measuring v a ruler, we find that 10 kilometers steps 2.4 cm. We can use this connection to discover the RF for the bar scale: ### 3. Determining scale from a Map or Photo

Some maps may come v no range at all. Aerial photographs practically never perform (unless one to be painted ~ above the ground prior to the photograph was taken!). How have the right to you derive a range for use v the map or photo?

Actually the procedure is very comparable to the last example above. But instead the measuring follow me a bar scale, you must measure the length of things on the map or photo whose actual length you know. This might be a football field, a city block, or the Equator (if it"s a human being map). Often you deserve to identify 1-mile-square sections in the us (see the account below, under survey Systems). You may even need to go the end to the ar mapped or pictured and measure the distance in between two i can identify objects.

Once you have the two distances, you can discover the scale as above. For an additional example, suppose you have actually a map wherein the distance in between two section-line roadways is 3.5 inch on the map. We deserve to usually i think this is one mile top top the floor (there are exceptions). The RF scale is then: One caveat (exception) because that air image is the this method assumes the two locations are in ~ the same elevation--or the the terrain is flat. If you are using waiting photos, the terrain may not it is in flat. If there room hills, even moderate ones, the calculations can be thrown off. Keep this in psychic for later in the course.

Another means to calculate scale on an unknown map or photograph is to compare it come a map v a well-known scale. For example, expect you have an air photo where the distance in between two hills is 7.2 centimeters.You have a map the the exact same area at 1:24,000, and on the map the distance between the hills is 2.4 centimeters.

The answer entails a small algebra. Due to the fact that the ground distance is the exact same on both photo and also map, we can produce an expression for this ground distance for both, and also then put them ~ above either side of an equation. The floor distance can be uncovered by multiplying the map/photo street by the scale (in this case, by the inverse of the scale--notice exactly how this provides the units cancel correctly). We must find, because that the photo, how plenty of ground devices are stood for by one unit ~ above the photo, so we use an x for this unknown quantity and also solve for it:  we deserve to cancel the systems on each side and divide through 7.2: In other words, the RF range for the photograph is 1:8,000.

### 4. Identify Distance and also Area from Map & Scale

Map range isn"t much use in and of itself. We can use a map"s range to identify distances and areas top top the map. Contrasted to converting in between scale types, calculating distance is simple. Area calculations space trickier, because we have to square the numbers.

Finding street from map and also scale

As an example, suppose we have actually a map v a range of 1:50,000. We measure the distance along a home boundary together 1.7 cm. What is the size in the actual world? To uncover ground distance, we have to use the map range to transform map distance to floor distance. An alert that again we inverted the RF scale, therefore the units will release properly. Once we main point by the scale, we require to transform the ground street to units suitable for ground measurement--in this case, indigenous centimeters to kilometers.

We can additionally calculate distance from verbal and also graphic scales. Through verbal scales, we usage the same procedure as above with the RF. The only distinction is that we need to use the units given in the verbal scale (e.g., 1 customs to 17 miles). We"d probably want to measure our map distance in the exact same units (in this case, inches) to do our switch easy.

Graphic scale are most likely the scale most frequently used by laypersons. You can mark turn off a street on the map and compare it directly to the bar scale. You need not know how many inches or centimeters the map street is. The key drawback that bar scales is that they room usually short compared to the map itself, and hence measure longer distances is difficult.

Finding area measurement native map and also scale

Area should be to express in areal units, which space usually distance systems squared -- cm2 , mi2, and also so on. We must as such used squared conversion components when detect area native map measurements.

For example, expect we measure a rectangular item of home that is 3 centimeter by 4 centimeter on a map. The map is in ~ a scale of 1:24,000. What is the area the the parcel?

The area that the package on the map is   on the ground.

Since this is a big number, we can want to translate to other units. There are 10,000 square meters per hectare, therefore the area is 69 hectares (ha) (a hectare is about 2.5 acres). Or, there space (1,000)2 = 1,000,000 square meters every square kilometer, so the area is additionally 0.69 km2.

Notice that by creating the units as part of the problem, and also squaring them in addition to the numbers, our systems cancel properly and we end up v a judicious answer.

There is another means to tackle area problems if you have actually distance dimensions choose 3 x 4 cm to start out the problem. You can convert the distance dimensions come real-world distances first, and also then main point them to discover the area. This provides the difficulty longer but perhaps simpler.

## B. Measurement scales

### 1. Definition

Any type of information on a map (or in a table, a list, a survey, etc.) have the right to be described in state of how pieces of the information have the right to be regarded each other. Instances of mapped information incorporate land-use classes, roadway classes, city populations, and county areas.

We have the right to think that these species of details as either categorical (or qualitative) or number (or quantitative). Categorical information have the right to only be explained qualitatively, whereas item of number information can be compared quantitatively. That is, numerical info is on a real scale, such 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 cannot say that based on the classes, 1 + 2 = 3 !We deserve to only use the numbering to explain the items qualitatively.Example of numerical information, city populations:Springfield = 100, Harmony = 200, Centerville = 300;We can say the Centerville has actually as many civilization as Springfield and Harmony.

### 2. Four Measurement Levels

The categorical and numerical species have traditionally been further broken down, each into two level of measurement:

Categorical information deserve to either it is in nominal level or ordinal level . At the in the name level, categories simply describe different varieties of things, and also cannot be contrasted to each other. Ordinal-level categories can, ~ above the various other hand, be ranked against each other.

An example of ordinal level would certainly be road classes of interstate, primary, secondary, and primitive; although two main roads don"t make an interstate, you could say in a sense that interstates space at a higher level than the others, at the very least in state of price to build!

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

Numerical information can either be interval level or ratio level . This distinction is subtle, and borders ~ above artificial. The only difference is the ratio-level info is top top a scale that consists of a true zero, the is, a zero that truly represents a absence of whatever it is you"re measuring.

One the the few common instances of one interval scale is temperature. You can compare two temperature readings quantitatively. For example, 20 C is 15 levels warmer than 5 C. But the Celsius scale has actually an arbitrary zero point (the freeze temperature of water, or 32 F). 0 C doesn"t mean a lack of temperature. Because that this reason, 20 C is not 4 times as warmth as 5 C! (One temperature scale, Kelvin, does feature a true zero -- 0 K is -273 C, the temperature in ~ which all molecular motion ceases). Fortunately, there are few examples that this top top maps. You could want to include an exception for elevation, which deserve to be below sea level, or longitude, whereby the 0° heat (Prime Meridian) is arbitrarily drawn on the globe.

Table 2: measure up Levels

 Measurement Level Description Examples Categorical Nominal Simple categories; can not rank categories Colors; land usage types; computer system components Categorical Ordinal Distinct categories; canrank categores in order Road classes; flavor preferences Numerical Interval Continuous scale; measure v numbers; realzero Temperature; longitude, compass direction Numerical Ratio Continuous scale; measurewith numbers; real zero Distance; weight; bank balance

Most number scales are ratio-level. We can compare 20 kilometres with 10 kilometres in any variety of ways, including saying the an initial is double as far as the second.

### 3. So What?

We will use this terminology typically to define the type of info on maps and also in various other sources. You will also encounter that elsewhere, i guarantee it!

Information regularly is analyzed from one level to another. The general ascendancy is the it"s less complicated to interpret to a reduced level (e.g., from proportion to ordinal) 보다 to a higher level. In most cases, it"s impossible to go legitimately come a higher level. Why bother making use of a lower-level scale? often it saves room and energy to use a reduced scale.

For example, if you have actually a table of city populaces in Sonoma ar (i.e., ratio level) and also want to show population on a map, you could print a number next to each city name. This would preserve your ratio-level data ~ above the map itself. A much more common technique is to have actually a set of increasingly big symbols for the city location, every symbol indicating a variety of population. These signs would offer ordinal-level information around population. This conveniently reduces the clutter top top the map, however you cannot recuperate the initial ratio-level numbers from the map.

## C. Accuracy, Precision, and far-ranging Digits

### 1. Accuracy matches Precision

Some world make a difference between accuracy and also precision.

Accuracy would certainly be just how close a measured worth is come the actual value.

Precision would be the number of digits reported through the value. Because that example, I included a thermometer to my car that mirrors the exterior temperature to one per 10 of a level (e.g., 65.2° F). The thermometer"s precision is to one per 10 of a level Fahrenheit. But it often seems to give readings that space too high, perhaps because of the engine"s warm nearby. That accuracy, then, might only it is in to within 5° F.

### 2. Far-reaching Digits

Significant digits room the variety of digits in a worth that have real an interpretation and reflect the accuracy the the worth or measurement. Because that example, a distance measurement of 45.8 kilometres would have three significant digits. The value means that the measurement was made to an accuracy of tenths of a kilometer. If the instrument, such together an odometer, is no accurate, the value should not encompass as many far-reaching digits. The course, if the instrument measures much more accurately 보다 this, the value have to be reported with the ideal precision.

The main allude is come beware dimensions with highly precise values when the accuracy could be called into question. This is particularly true as soon as converting worths from one type of range to another. For example, if ns measure a map street as 11 inches v 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 suggests high accuracy, which i didn"t have actually with the original measurement. The solution below is to ring the price to about the very same number of far-ranging digits together the original measurement. In this case, i should most likely say the distance is 28 cm.

More example of far-reaching digits:

Two far-ranging 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 kind of other digits. Normally, zeroes to the appropriate of various other digits (e.g., 3700) room not thought about significant, uneven a decimal suggest is added and more zeroes happen to the best of the (e.g., 3700.0 means 5 significant digits). What if we have a measurement of 1900 wherein the zeroes are significant? Traditionally, a bar is inserted over the zeroes to indicate significance.

Another systems is to use scientific notation.

For example, 3700 through the zeroes in reality being far-ranging can be written as 3.700 x 103. This division the number down right into the mantissa (the significant digits, here 3.700) and also the exponent ~ above the ten (here 3). In clinical notation, only one number is placed prior to the decimal suggest in the mantissa. The exponent ~ above the 10 shows how countless places the decimal point should be relocated to regain the number to simple notation (in this case, three places to the right; this is tantamount to multiplying the mantissa by 1000). An unfavorable exponents mean smaller numbers, and we transition the decimal allude to the left. Because that example, 3.700 x 10-4 is the same as 0.0003700. Scientific notation is handy v very huge or little numbers. Numbers in clinical notation can be used as with other numbers, as lengthy as you monitor the rule of exponents -- because that multiplying, dividing, etc.

## D. Classification, Simplification and Symbolization of Data

This is no a food in cartography, so we will certainly not transaction in detail with just how data is classified and also simplified for mapping, and how symbols are created to fit those data. But you have to be mindful that any map, consisting of topographic maps, is the result of a lot of processing of the data behind the map. Here is a quick discussion the some elements that go into data processing for maps.

### 1. Classification

Maps have to take the pertinent data and assign it to a given variety of classes, each v its own variety of members. Instances are maps of floor uses and of temperature. For categorical data favor land uses, the is basic to overload the map reader v too numerous classes. Cartographers introduce a best of five or six various classes (for floor use, these can be forest, rangeland, cropland, water, and urban). Number data shown on isarithmic maps (which show zones of same values) have the right to be somewhat much more complex. Because that example, temperature zones have the right to trend native 80"s F come -20"s F. But the data must be presented with logical symbolization (see below).

Data have the right to be broken down into categories in three ways:

(a) Each category can have an equal variety of members. For example, in a map the US populace by state, we could have 5 categories the population, each with ten states.

(b) Each classification could expectancy an same interval the values. In the populace map, we would certainly take the variety of populaces (highest state minus shortest state), and divide the variety by five. Each classification would be one-fifth the the as whole range. In this map, categories might have various numbers that states. The highest classification may only have a couple of states (e.g., California, brand-new York and also Texas), and also other category may have a huge number of states.

(c) Finally, we could subjectively assign states to classes, maybe by trying to find "natural breaks" in population rankings. Often map-makers begin out with among the first two methods, then refine the by looking in ~ the outcomes and an altering classes slightly. All of this should reflect the objectives of the map. Different methods can develop radically different-looking maps (see any cartography message for examples).

### 2. Simplification

A second major task in map-making is simplifying the details behind the map. Group is one means of simple the data we use going into the map. Often this involves lowering the measure up level that the data (such as transforming ratio-level data come ordinal-level data, as in our instance of city populations shown by various circle sizes).

Another simplification task relates come the spatial facets of the data. For example, mountainous roads might take numerous twists and turns. A map that shows all this curves would certainly be cluttered and also messy. We might want come generalize the roadway spatially come clarify things. Beware, the course, those map users who curse you because that those curve they didn"t expect! The cartographer"s task is to simplify without distorting and also misleading the map user.

Sometimes the task might necessitate eliminating features altogether. For example, a small-scale united state map can show only selected cities; just how do you select which cities to include without offending too plenty of people? I experienced a us map recently that included moderate-sized cities yet omitted my hometown, san Diego (now the sixth largest city in the US).

### 3. Symbolization

Symbolization of details is another an important part of interacting through maps. What icons are chosen will influence whether will human being will understand, or also use, a map. Symbols have to be preferred so the the to plan audience will know them. Various symbols need to be used for general-purpose maps than those to plan for professionals in a field.

Symbols can be put on a continuum in between intuitive and also abstract. Intuitive symbols indicate to the reader what they represent. Pictographs are recognizable depictions of the actual objects. For example, marshes space often shown with swampy grass symbols, or airports together planes. Top top the other extreme are abstract icons with no apparent connection to what they represent. Examples are circles as cities, or streams together dotted lines. Part abstract symbols have actually been supplied so commonly to stand for a specific feature that, although abstract, they do connect with the object in most people"s minds. A star within a circle, because that instance, usually method a funding city.

Symbols can also be classed according to their dimension: point (0-dimension), heat (1-dimension) or area (2-dimension) symbols. Prefer the various other two, point symbols deserve to convey categorical or number information. Examples of categorical point symbols are 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 usage of lines on maps room isolines. Isolines (also dubbed isarithms) connect points of equal value. You"ll regularly see this on a map of temperature on the weather page of the newspaper. Every ar along an isoline top top this map has the same temperature, at the very least theoretically. This implies also that places between two isolines have values somewhere in between the worths of the bordering lines. Without extr information, us cannot say v confidence much more about intervening values. We have the right to estimate, or interpolate, the intervening values, for instance by measure the distance of a point from every line. Over there is no guarantee, the course, that our calculation is yes, really correct, so beware such estimates from isoline maps. An important form of isoline because that this course is the elevation edge . This isolines show equal elevations, and are included on all 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 on 1:24,000-scale maps room 20, 40 and 80 feet. A 20-foot interval would show, because that example, border at 0 (sea level), 20, 40, 60, 80, and also so on.

It take away some exercise to feel comfortable working v elevation contours and other isoline maps. We will have lab exercises to provide you some practice with them, consisting of visualizing terrain and constructing profiles, or two-dimensional views of exactly how elevation changes on a line across the topographic map.

The zones between isolines are regularly shaded or fancy to portray the information much more effectively. Temperature maps in many newspapers are now in color, through warmer zones obtaining "warmer" colors, colder areas "cooler" colors. These shaded-isoline zones are a mix of line and also area symbols.

Speaking of color and also shading, let us cover one last point around map symbolization. The rules about 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 specific order, and you probably want to maximize the contrast in between categories. Soil uses, because that example, need to be depicted so the you have the right to separate urban, suburban, forest, and pasture, or everything categories you incorporate on the map.

Ordinal, term or ratio data have to be mapped differently. Right here there is a identify ordering that categories. To use the temperature map again, we have actually a tendency from warm to cold in the zones we portray. We desire the map leader to automatically appreciate this progressive trend in the data. Therefore we pick an notified of colour or symbols that conveys this consistent trend in the data, for example: red-orange-yellow-green-blue-violet.

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

Many world make the wrong of reasoning they should pick colors that maximize contrast between categories, also with ordinal or higher-level data. Beware this mistake! you may have the ability to pick out categories quickly with this approach, however you destroy the impression of a trend in the data.