Geographical Techniques Questions and Answers

Answer: D

The scale should be 1 : 6,360.

One acre is about 4,047 square metres. If it is to occupy 1 square centimetre, the side of that square (1 cm on the map) must represent the side of a square acre on the ground:

\[ \begin{aligned} \text{side} &= \sqrt{4047\ \text{m}^{2}} \\ &\approx 63.6\ \text{m} = 6360\ \text{cm} \end{aligned} \]

So 1 cm on the map stands for about 6,360 cm on the ground, a scale of 1 : 6,360.

The other options are rounded or misworked values. 1 : 5,000 and 1 : 5,500 would make 1 square cm represent only about 0.62 and 0.75 acre, and 1 : 6,000 about 0.89 acre, so the minimum mapping unit would come out smaller than one acre.

Answer: A

The monitor can show 16777216 shades.

A quantization level of \(2^{8}\) means each band is recorded in 8 bits, giving 256 brightness values (0 to 255). When three bands are displayed through the red, green and blue guns of a monitor, every combination of the three values is a distinct colour:

\[ \begin{aligned} N &= 256^{3} = 2^{24} \\ &= 16{,}777{,}216 \end{aligned} \]

This is the familiar 24-bit 'true colour' of computer displays. The other figures, 1677216, 1677816 and 72167716, are miscopied versions of this number with a digit dropped, changed or scrambled, and none equals \(256^{3}\).

Answer: C

The key's answer is Near infrared is represented as red.

In a standard false colour composite (FCC), the near infrared band is displayed through the red channel, the red band through the green channel and the green band through the blue channel. Healthy vegetation reflects near infrared very strongly, because of the internal structure of the leaf, so it is very bright in the band that has been assigned to red, and therefore appears red on the image.

Vegetation does reflect near infrared, but that alone would not make it look red, since near infrared is invisible; it is the assignment of that band to red that produces the colour, which is the point the key takes. Vegetation reflecting green explains why it looks green to the eye and in a true colour image, not in an FCC. 'Red is represented as green' is part of the FCC scheme but explains the colour of other features, not the red of vegetation.

Answer: A

The colour with the highest frequency among those listed is blue.

For light, frequency and wavelength are inversely related: \(f = c/\lambda\), where c is the speed of light. The shorter the wavelength, the higher the frequency. In the visible spectrum blue light has a wavelength of roughly 450 to 495 nm, shorter than green (about 495 to 570 nm), yellow (about 570 to 590 nm) and red (about 620 to 750 nm).

So blue has the highest frequency of the four, and red, with the longest wavelength, has the lowest. Violet, at the very short end of the spectrum, would be higher still, but it is not among the options; green and yellow lie between blue and red.

Answer: D

The mean is called the most balanced measure because the sum of deviations from it equals zero.

For any set of values, the deviations above the arithmetic mean exactly cancel those below it:

\[ \sum_{i=1}^{n} (x_{i} - \bar{x}) = 0 \]

The mean is therefore the point at which the data balance, like the centre of gravity of weights placed along a beam, and that property is what 'balanced' refers to.

The other options are wrong or beside the point. The centre of the range is the mid-range, which the mean need not equal. All values do take part in calculating the mean, but that makes it comprehensive rather than balanced. And the mean is strongly affected by extreme values, which is its chief weakness compared with the median.

Answer: C

Such data are generally represented on an isopleth map.

Values measured at points, such as temperature, rainfall or elevation, are treated as samples of a continuous surface, which is how a raster represents data. Isopleths (isolines) are drawn through interpolated points of equal value, so they show exactly this kind of continuously varying data, as isotherms, isohyets and contours do.

A choropleth map shades whole administrative areas by a value per unit area. Chorochromatic maps colour areas by qualitative category (such as soil type), and choroschematic maps use symbols for qualitative distributions; neither is built from continuous point data.

Answer: C

The image co-ordinate system starts at the top left corner.

A digital image is a grid of pixels stored row by row, as it is scanned or displayed. Its co-ordinate origin (row 0 or 1, column 0 or 1) is therefore the upper left pixel; column numbers increase to the right and row numbers increase downwards.

This differs from the usual map or Cartesian convention, in which the origin is at the bottom left and y increases upwards, which is why the bottom left option is the common mistake. Georeferencing has to account for that flipped row axis.

Answer: B

Georeferencing involves assigning geographical co-ordinates to the mapped units.

A scanned map or a satellite image starts with only image co-ordinates (rows and columns). Georeferencing ties it to the real world by identifying ground control points whose latitude and longitude, or projected co-ordinates, are known, and transforming the image so that every location carries real geographical co-ordinates in a defined projection.

Attaching attribute data is attribute entry, linking non-spatial information to features. 'Spatial data' is too vague, since the data are already spatial, and real-time data feeds are a different matter entirely.

Answer: D

The mean of the squared deviations is the variance.

For \(n\) values with mean \(\bar{x}\):

\[ \sigma^{2} = \frac{\sum (x_{i} - \bar{x})^{2}}{n} \]

Squaring the deviations stops positive and negative ones from cancelling. The standard deviation is the square root of the variance, which puts the spread back in the original units, so it is not the mean of the squares itself. The arithmetic mean is the average of the values, and the mode is the most frequent value.

Answer: C

The expression is the geometric mean.

The geometric mean of \(n\) positive values is the \(n\)th root of their product:

\[ G = \sqrt[n]{a_{1} a_{2} a_{3} \cdots a_{n}} \]

For example, the geometric mean of 2 and 8 is \(\sqrt{16} = 4\). It suits growth rates and ratios.

The arithmetic mean adds the values and divides by \(n\); the harmonic mean is \(n\) divided by the sum of the reciprocals. 'Absolute mean' is not a standard average.