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Numerical Skills
See if you can get ten out of ten in this quiz.

Numerical Skills

A key feature of fieldwork assessment is your ability to handle data to draw informed conclusions. Part of data handling is presentation, but this Geography quiz concentrates on the numerical skills that are required for the GCSE. These skills will be assessed in your written exams as well as in your fieldwork. It will be worth having a pen, paper and calculator handy before starting the quiz.

You need to demonstrate that you understand areas and scales and are aware of the relationships between units, a simple example of this could be the relationship between metres and kilometres or hectares and square metres. The two common map scales that you will use at GCSE are 1:50,000 and 1:25,000 - you should know that these mean that one centimetre on the map represents 50,000 cm (0.5 km) or 25,000 cm (0.25 km) on the ground. Each square on an OS map grid represents an area of one square kilometre.

When designing your fieldwork, you need to be able to design data collection sheets before you start. An example of this would be if you were studying water flow at the edge and in the centre of a stream. A suitable table would include a column for the distance from the starting point of your survey with two columns for flow rate, one for the edge and the other for the centre. Data collection sheets can be modified if you don't get them quite right, but you will be required to explain why you changed them in your evaluation. You won't lose marks but you could easily gain them for doing that. Your planning also needs to show that you appreciate ways of ensuring that your data is as accurate and reliable as possible for example, repeat readings or comparing with a control group as appropriate.

When processing numerical data, you will need to use a number of valid statistical techniques, including appropriate measures of central tendency, spread and cumulative frequency (in other words - median, mean, range, quartiles and inter-quartile range, mode and modal class). Being able to work out and use percentiles, percentage increases and percentage decreases is essential, but once you get the hang of it, it's not actually too difficult. At the highest levels, you need to be able to spot weaknesses in selective statistical presentation of data.

Finally, when processing bivariate data (that's the posh way of saying data that includes two variables), not only should you be able to identify and draw trend lines on a graph, you should be able to work out gradients and use the trend lines to describe any correlation between data sets and extrapolate and interpolate the trends you have identified. But don't get too stressed about this, you will already have done loads of this in maths and science lessons as well.

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1.
On an OS map, what area would be represented by a block that measured 4 grid squares long and 3 grid squares wide?
12 km2
12 hectares
12 m2
120,000 m2
A grid square on an OS map represents one square kilometre on the ground
2.
What is the range of these numbers: 8, 7, 5, 9, 3, 5, 6, 4, 6, 6?
8
4.8
6
5.9
The range is the difference between the largest and smallest number
3.
Which of the following distances are equivalent?
1 km and 100 m
5 km and 5000 m
1.5 km and 1500 cm
18.6 km and 186,000 m
You need to be able to correctly convert from one SI unit to another
4.
What is the mean of these numbers: 8, 7, 5, 9, 3, 5, 6, 4, 6, 6?
8
4.8
6
5.9
The mean is also called the arithmetic mean or the average and is one measure of central tendency
5.
What is the mode of these numbers: 8, 7, 5, 9, 3, 5, 6, 4, 6, 6?
8
4.8
6
5.9
The mode (or modal value) is simply the number that appears in the list most frequently
6.
Which of the following is NOT correct?
One hectare is equal to ten thousand square metres
5 ha = 0.05 km2
One kilometre is represented by 25 centimetres on a map drawn to a scale of 1:25,000
The summit of a 500m high hill is 0.5 km above sea level
Make sure that you revise the meaning of map scales
7.
The GDP of Bangladesh in 2014 was 173 billion US dollars. In 2015, this had increased to 195 billion US dollars. What is the approximate percentage increase?
10%
13%
16%
19%
You can forget about the units for the calculation as you are just working out a percentage. You don't need to write all of the zeros to represent the billion as they are the units. The increase in GDP is 22 (195 - 173). The original value is 173. The percentage increase is therefore 22 divided by 173 multiplied by 100 to get the percentage. This works out at 12.7 so the closest answer is 13%
8.
A class was asked to prepare an isoline map showing the pedestrian flow around the CBD of their local town using 5 minute pedestrian counts. They split up and everyone made their observations at 1pm. Which of the following would be the most useful columns for putting the class results into a table?
Number of pedestrians, distance from centre of the CBD
Number of pedestrians, distance from centre of the CBD and time
Number of pedestrians, distance from centre of the CBD, number of businesses visited by at least one pedestrian
Number of pedestrians and time
An isoline map is designed to present bivariate data, so only two columns are needed. The time at which each count was made was the same, so it is not necessary to record it in the table of results
9.
Which of the following statements is NOT true?
You should make as many repeat measurements in the time available so that you can evaluate how accurate and reliable your results are
Taking an average of each of the results will help to make your data more accurate as it can smooth out errors
Taking a single set of results makes it hard to evaluate if your results are accurate
If you concentrate, taking only a single set of results guarantees that they will be accurate and reliable
Accuracy and reliability are not the same
10.
What is the median of these numbers: 8, 7, 5, 9, 3, 5, 6, 4, 6, 6?
8
4.8
6
5.9
When there are an even number of results, the median is the mean of the two central numbers, in this case 6 and 6. It is also referred to as the 50th percentile
Author:  Kev Woodward

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