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A. Map Scale

B. Measure up Scales

C. Accuracy, Precision, and far-reaching Digits

D. Classification, Simplification and Symbolization the Data

## A. Map range

Map range is the relationship in between a unit of size on a map and also the equivalent length top top the ground. We will use principles of map range throughout the course, for this reason it will pay girlfriend to study 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 ground with three different varieties of scale. Verbal range expresses in native a relationship between a map distance and a soil distance. Typically it is along the present of:

One inch represents 16 miles.

Here that is implied the the one inch is on the map, and that one customs represents 16 miles on the ground. Linguistic scales are typically found on famous atlases and also maps.

The second type of scale is a graphic scale, or bar scale. This shows directly on the map the corresponding ground distance. Because that example:

The third kind of scale is a representative fraction, or ratio scale. Compared to the first two, the is the many abstract, but likewise the most versatile. A representative fraction, or RF, mirrors the relationship in between one of any unit ~ above the map and one of the very same unit on the ground. RFs may be presented as an really fraction, for instance 1/24,000, yet are normally 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.) on the map represents 24,000 that those same units ~ above the ground (24,000 mm, 24,000 cm, 24,000", 24,000", etc.). The RF is versatile due to the fact that you room not tied come any details units. You may work in any kind of unit you choose, one of two people metric, English, or other.

The RF is a referred to as a fraction because it is just that--a fraction that shows exactly how much the real people is reduced to fit on the map. A good comparison is often made with scale models of automobiles or aircraft. A 1/32-model of an auto is 1/32nd as large as the yes, really auto. In the same way, a 1:100,000-scale map is 1/100,000th as big as the soil area shown on the map.

A related idea is that of small scale versus large scale. Geographers use these terms in different way than many people. A big scale map is where the RF is relatively large. A 1:1200 map is as such larger scale than a 1:1,000,000 map. The 1:1,000,000 map would generally be referred to as 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 rule of thumb for dimension of scale by RF:

Size the 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 big scale is relative. I noticed a surveying text (Brinker & Wolf, 1984) that classed anything smaller than 1:12,000 as tiny scale -- surveyors rarely job-related with anything smaller than this.

The large/small scale terminology can become confusing once talking about huge versus little areas. If you space talking about a phenomenon that occurs throughout a large region, that is tempting come say it"s a massive phenomenon (e.g., "the woodland blight is a large-scale disease"). But because the map that would display this would be small-scale, that is better to usage a various term to stop confusion. My favourite is "broad-scale."

Many maps incorporate two or even all three types of scales. USGS topographic maps have both bar scales and also RFs.

### 2. Converting between Scale Types

If you are provided one type of scale, friend should have the ability to derive or construct any of the various other two. This takes some practice, and also some troubles are had in her lab exercises. Some examples are given below.

A crucial step in doing any kind of kind of counter that involves differing systems is to include the devices in the difficulty itself. You deserve to then publication the devices by multiplying or dividing. This way you avoid ending up being confused around which conversion components to use and how to usage them.

Verbal scale to RF

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

(a) transform verbal scale of "1" come 18 miles" to RF

or 1:1,140,000.

Notice the the resulting fraction is rounded so that the RF does not imply much more accuracy 보다 the original precision warranted.

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

or 1:6700.

In countless conversions you can save steps if you remember additional equivalencies.

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

Verbal range to graphics Scale

Usually this is a reasonably easy job if the map offers us reasonable systems in the verbal scale. We deserve to use the linguistic scale prefer a fraction to change the ground street to map distance.

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

One centimeter is a reasonably small distance, so we most likely don"t want our bar range to have major divisions much smaller 보다 this. A centimeter to represent 14 km, therefore a department of 10 kilometres is most likely fine. Thus we want to uncover how many centimeters represent 10 km.

In other words, we have the right to represent ours 10 kilometres increment ~ above the bar range by measuring off 0.71 cm on the map. We"d draw the an initial tick in ~ 0.71 cm, the second at 1.42 cm, and also so on:

RF to Graphic Scale

This add to an extra step to the instance above. Us can find the map-distance indistinguishable of a ground distance, however we also need to it is in careful around choosing which ground street we desire to portray on the map. Probably it"s most basic to pick a smaller sized ground street that you have the right to then main point to acquire a reasonable bar scale.

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

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

This might work fine, v one mile significant off top top the map every 0.25 inch; or, we might want finer or broader increments, which us can find by dividing or multiply the .25" together needed.

RF to linguistic Scale

Again we have to choose appropriate units to convert into. Many verbal scales room either "one inch represents ____ miles," or "one centimeter represents ___ kilometers." these are relatively easy come do, due to the fact that it method only the we transform the denominator of ours RF to the larger units.

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

Therefore,

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

Graphic range to RF

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

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

By measuring with a ruler, we find that 10 kilometers procedures 2.4 cm. We deserve to use this connection to uncover the RF for the bar scale:

### 3. Determining range from a Map or Photo

Some maps might come through no range at all. Aerial photographs practically never execute (unless one to be painted top top the ground before the photograph was taken!). How have the right to you derive a scale for use through the map or photo?

Actually the procedure is very comparable to the last instance above. Yet instead of measuring along a bar scale, you have to measure the length of an object on the map or picture whose actual length you know. This can be a football field, a city block, or the Equator (if it"s a human being map). Regularly you deserve to identify 1-mile-square part in the united state (see the account below, under survey Systems). Girlfriend may also need come go out to the location mapped or pictured and also measure the distance in between two i can identify objects.

Once you have the two distances, girlfriend can uncover the scale as above. For another example, intend you have a map wherein the distance in between two section-line roadways is 3.5 inches on the map. We have the right to usually assume this is one mile ~ above the ground (there space exceptions). The RF range is then:

One caveat (exception) for air picture is that this technique assumes the two places are at the same elevation--or that the terrain is flat. If you room using waiting photos, the terrain might not be flat. If there are hills, also moderate ones, the calculations can be thrown off. Store this in mental for later on in the course.

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

The answer involves a tiny algebra. Due to the fact that the ground distance is the same on both photo and also map, we can develop an expression because that this ground distance for both, and then put them ~ above either next of an equation. The ground distance deserve to be uncovered by multiply the map/photo street by the scale (in this case, through the train station of the scale--notice exactly how this makes the units cancel correctly). We should find, because that the photo, how plenty of ground units are represented by one unit on the photo, for this reason we use an x for this unknown quantity and also solve because that it:

we have the right to cancel the systems on every side and divide through 7.2:

In other words, the RF range for the photograph is 1:8,000.

### 4. Determining Distance and Area native Map & Scale

Map scale isn"t lot use in and also of itself. We deserve to use a map"s scale to recognize distances and areas top top the map. Contrasted to converting between scale types, calculating distance is simple. Area calculations are trickier, because we need to square the numbers.

Finding street from map and scale

As an example, mean we have actually a map through a range of 1:50,000. We measure the distance along a residential or commercial property boundary as 1.7 cm. What is the size in the genuine world?

To discover ground distance, we should use the map range to convert map distance to floor distance. Notification that again we inverted the RF scale, for this reason the devices 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 come kilometers.

We can likewise calculate street from verbal and also graphic scales. Through verbal scales, we use the same procedure as above with the RF. The only difference is that we have to use the units provided in the verbal scale (e.g., 1 customs to 17 miles). We"d more than likely want to measure our map distance in the same units (in this case, inches) to do our switch easy.

Graphic scale are more than likely the scale most typically used by laypersons. You deserve to mark off a street on the map and also compare it directly to the bar scale. You require not recognize how numerous inches or centimeters the map distance is. The key drawback of bar scales is the they are usually short compared to the map itself, and also hence measure longer ranges is difficult.

Finding area measurement indigenous map and scale

Area need to be express in areal units, which space usually distance units squared -- cm2 , mi2, and so on. We must therefore used squared conversion components when finding area native map measurements.

For example, mean we measure a rectangular item of residential property that is 3 cm by 4 centimeter on a map. The map is in ~ a range of 1:24,000. What is the area that the parcel?

The area of the package on the map is

on the ground.

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

Notice the by creating the devices as component of the problem, and squaring them in addition to the numbers, our systems cancel properly and we finish up through a cautious answer.

There is another way to handle area problems if you have actually distance dimensions prefer 3 x 4 cm to start out the problem. You can convert the distance dimensions come real-world ranges first, and then multiply them to uncover the area. This provides the trouble longer however perhaps simpler.

## B. Measurement scale

### 1. Definition

Any kind of info on a map (or in a table, a list, a survey, etc.) have the right to be explained in state of exactly how pieces of the information can be concerned each other. Instances of mapped information include land-use classes, road classes, city populations, and county areas.

We can think that these species of information as one of two people categorical (or qualitative) or numerical (or quantitative). Categorical information have the right to only be defined qualitatively, whereas item of number information have the right to be compared quantitatively. That is, numerical information is ~ above a genuine scale, together as distance (e.g., kilometers), area (e.g., hectares), or temperature (e.g., Celsius).

Example that 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 use the numbering to define the items qualitatively.Example of numerical information, city populations:Springfield = 100, Harmony = 200, Centerville = 300;We have the right to say the Centerville has actually as many civilization as Springfield and also Harmony.

### 2. 4 Measurement Levels

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

Categorical information can either it is in nominal level or ordinal level . In ~ the in the name of level, category simply explain different species of things, and cannot be compared to each other. Ordinal-level categories can, top top the various other hand, be ranked against each other.

An example of ordinal level would be roadway classes the interstate, primary, secondary, and primitive; although two main roads don"t make an interstate, you can say in a feeling that interstates space at a greater level 보다 the others, at the very least in state of price to build!

The land-use classes would certainly be an example of nominal-level measurement. You more than likely wouldn"t rank the classes versus each various other (unless you prefer one end the other, in which case they can be ordinal!).

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

One that the couple of common examples of one interval scale is temperature. You deserve to compare two temperature readings quantitatively. For example, 20 C is 15 degrees warmer 보다 5 C. However the Celsius scale has an arbitrarily zero point (the freezing temperature that water, or 32 F). 0 C doesn"t mean a lack of temperature. Because that this reason, 20 C is not four times as warm as 5 C! (One temperature scale, Kelvin, does function a true zero -- 0 K is -273 C, the temperature in ~ which all molecular movement ceases). Fortunately, there are couple of examples that this on maps. You could want to encompass an exception for elevation, which have the right to be listed 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 components Categorical Ordinal Distinct categories; canrank categores in order Road classes; odor preferences Numerical Interval Continuous scale; measure with numbers; realzero Temperature; longitude, compass direction Numerical Ratio Continuous scale; measurewith numbers; genuine zero Distance; weight; bank balance

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

### 3. For this reason What?

We will usage this terminology frequently to describe the kinds of information on maps and in various other sources. Friend will likewise encounter the elsewhere, i guarantee it!

Information regularly is translated from one level come another. The general dominion is that it"s simpler to translate to a lower level (e.g., from proportion to ordinal) 보다 to a higher level. In most cases, it"s difficult to walk legitimately come a greater level. Why bother utilizing a lower-level scale? regularly it saves an are and power to usage a lower scale.

For example, if you have actually a table of city populations in Sonoma ar (i.e., ratio level) and also want come show populace on a map, you can print a number alongside each city name. This would maintain your ratio-level data top top the map itself. A more common method is to have actually a set of increasingly huge symbols because that the city location, every symbol describe a range of population. These signs would offer ordinal-level information about population. This conveniently reduces the clutter ~ above the map, however you cannot recover the original ratio-level number from the map.

## C. Accuracy, Precision, and significant Digits

### 1. Accuracy matches Precision

Some people make a distinction between accuracy and precision.

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

Precision would certainly be the variety of digits reported v the value. For example, I included a thermometer come my car that shows the outside temperature to tenths of a level (e.g., 65.2° F). The thermometer"s precision is to tenths of a degree Fahrenheit. But it regularly seems to offer readings that are too high, perhaps as result of the engine"s heat nearby. That is accuracy, then, might only it is in to in ~ 5° F.

### 2. Far-ranging Digits

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

The main point is come beware dimensions with highly specific values once the accuracy can be dubbed into question. This is especially true as soon as converting worths from one kind of range to another. For example, if ns measure a map distance as 11 inches v an simple ruler, then want to transform to centimeters, I discover on mine 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 below is to round the price to about the very same number of far-ranging digits together the original measurement. In this case, ns should more than likely say the distance is 28 cm.

More instance 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 added after the decimal point imply precision equal to any kind of other digits. Normally, zeroes to the right of various other digits (e.g., 3700) room not taken into consideration significant, uneven a decimal allude is added and much more zeroes occur to the best of it (e.g., 3700.0 implies 5 far-ranging digits). What if we have actually a measurement of 1900 wherein the zeroes space significant? Traditionally, a bar is put over the zeroes to show significance.

Another systems is come use clinical notation.

For example, 3700 v the zeroes in reality being far-reaching can be written as 3.700 x 103. This breaks the number down into the mantissa (the far-reaching digits, below 3.700) and the exponent ~ above the ten (here 3). In clinical notation, just one digit is placed prior to the decimal allude in the mantissa. The exponent on the 10 shows how numerous places the decimal allude should be relocated to restore the number to simple notation (in this case, three places to the right; this is identical to multiply the mantissa by 1000). An unfavorable exponents typical smaller numbers, and also we transition the decimal allude to the left. Because that example, 3.700 x 10-4 is the exact same as 0.0003700. Clinical notation is handy through very big or tiny numbers. Numbers in scientific notation have the right to be used as with other numbers, as long as you monitor the rules of index number -- because that multiplying, dividing, etc.

## D. Classification, Simplification and also Symbolization the Data

This is not a food in cartography, for this reason we will not transaction in detail with just how data is classified and simplified for mapping, and how symbols are developed to fit those data. But you must be conscious that any kind of map, including topographic maps, is the result of a many processing that the data behind the map. Below is a quick discussion the some elements that go into data handling for maps.

### 1. Classification

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

Data deserve to be broken down into categories in three ways:

(a) Each category can have actually an equal variety of members. Because that example, in a map that US population by state, we might have 5 categories of population, each through ten states.

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

(c) Finally, we might subjectively assign claims to classes, possibly by looking for "natural breaks" in populace rankings. Frequently map-makers begin out with one of the very first two methods, climate refine that by looking at the outcomes and an altering classes slightly. All of this should reflect the functions of the map. Different methods can develop 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 usage going into the map. Regularly this involves lowering the measure up level the the data (such as transforming ratio-level data come ordinal-level data, together in our instance of city populations shown by miscellaneous circle sizes).

Another simplification job relates to the spatial aspects of the data. For example, such as mountain roads might take many twists and also turns. A map that reflects all these curves would certainly be cluttered and also messy. We might want come generalize the roadway spatially to clarify things. Beware, the course, those map individuals who 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 task might necessitate eliminating features altogether. Because that example, a small-scale united state map can present only selected cities; exactly how do you select which cities to incorporate without offending too many people? I witnessed a us map newly that contained moderate-sized cities yet omitted my hometown, mountain Diego (now the 6th largest city in the US).

### 3. Symbolization

Symbolization of details is another an important part of connecting through maps. What icons are preferred will affect whether will human being will understand, or even use, a map. Symbols have to be liked so that the intended audience will know them. Different symbols need to be supplied for general-purpose maps 보다 those plan for experts in a field.

Symbols can be placed on a continuum between intuitive and abstract. Intuitive symbols indicate to the leader what castle represent. Pictographs room recognizable representations of the really objects. For example, marshes are often displayed with swampy grass symbols, or airports together planes. On the other too much are abstract signs with no noticeable connection come what lock represent. Instances are circles together cities, or streams together dotted lines. Some abstract symbols have been offered so widely to stand for a specific feature that, although abstract, lock do attach with the object in many people"s minds. A star in ~ a circle, for instance, usually way a capital city.

Symbols can likewise be classed follow to your dimension: suggest (0-dimension), line (1-dimension) or area (2-dimension) symbols. Like the other two, suggest symbols have the right to convey categorical or number information. Examples of categorical allude symbols room airports, campgrounds, springs, and quarries. Variable-sized circles because that city populace would be instances of numerical point symbols.

Line symbols can convey information around linear features, such together roads, railroads, and also streams. One more important usage of currently on maps room isolines. Isolines (also called isarithms) attach points of same value. You"ll frequently see these on a map of temperature on the weather web page of the newspaper. Every place along one isoline top top this map has actually the very same temperature, at the very least theoretically. This implies also that places in between two isolines have values somewhere between the worths of the bordering lines. Without extr information, we cannot say through confidence much an ext about intervening values. We deserve to estimate, or interpolate, the intervening values, for example by measure the street of a point from every line. There is no guarantee, the course, that our estimate is yes, really correct, so beware such estimates from isoline maps.

An important kind of isoline because that this food is the elevation edge . These isolines display equal elevations, and are included on every USGS topographic maps. The edge interval is the elevation difference in between each contour. Contour intervals top top USGS maps vary relying on the terrain. Common intervals top top 1:24,000-scale maps space 20, 40 and 80 feet. A 20-foot interval would certainly show, because that example, contours at 0 (sea level), 20, 40, 60, 80, and so on.

It bring away some practice to feeling comfortable working v elevation contours and other isoline maps. Us will have actually lab practice to give you some practice with them, including visualizing terrain and also constructing profiles, or two-dimensional see of exactly how elevation alters on a line throughout the topographic map.

The zones between isolines are often shaded or colored to portray the information more effectively. Temperature maps in many newspapers are now in color, v warmer zones obtaining "warmer" colors, colder locations "cooler" colors. This shaded-isoline zones space a blend of line and area symbols.

Speaking that color and shading, let us cover one final point around map symbolization. The rules around using color and also shading are different for nominal matches higher-level data (ordinal, interval, and ratio). If you space mapping nominal-level data, the categories have actually no certain order, and you most likely want to maximize the contrast in between categories. Land uses, because that example, need to be shown so the you can separate urban, suburban, forest, and pasture, or everything categories you incorporate on the map.

Ordinal, term or proportion data must be mapped differently. Below there is a identify ordering the categories. To use the temperature map again, we have 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 select an bespeak of color or signs that conveys this constant trend in the data, for example: red-orange-yellow-green-blue-violet.

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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 be able to pick out categories easily with this approach, but you ruin the impression the a tendency in the data.