➖ Mean
Add up every value, then divide by the number of values. It uses every result, but one very high or low result can pull it away from the rest.
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Unlock This CourseYou have planned your enquiry, collected your data and presented it. Now comes the thinking. Section B of the exam rewards students who can explain what their results show and how far they can be trusted. The spec calls these the cognitive enquiry skills.
Key terms:
Good analysis uses both kinds of data. Look at the numbers (quantitative) and at the sketches, photographs and comments (qualitative). Then ask three questions:
Use figures from your results when you describe a pattern. "Pebbles get smaller" is weak. "Pebbles fall from a mean of 60 mm at site 1 to a mean of 20 mm at site 5" is strong.
Statistics boil a list of results down to one or two useful numbers.
Add up every value, then divide by the number of values. It uses every result, but one very high or low result can pull it away from the rest.
Put the values in order and take the middle one. If there are two middle values, find the number halfway between them. One odd result has little effect on the median.
The most common value. It is useful when you want the typical result, such as the most common answer to a questionnaire.
Highest minus lowest. A big range means the results are spread out. A small range means they are close together.
A student measured the longest axis of nine pebbles on a beach (in mm): 12, 15, 9, 15, 20, 11, 15, 13, 10.
Mean: 12 + 15 + 9 + 15 + 20 + 11 + 15 + 13 + 10 = 120. Then 120 ÷ 9 = 13.3 mm (to 1 decimal place).
Median: in order the values are 9, 10, 11, 12, 13, 15, 15, 15, 20. The middle (5th) value is 13 mm.
Mode: 15 mm appears three times, so the mode is 15 mm.
Range: 20 − 9 = 11 mm.
A scatter graph plots one measurement against another, such as distance downstream against river width. If the points slope upwards, there is a positive relationship: as one rises, so does the other. If they slope downwards, the relationship is negative.
A line of best fit shows the trend. Draw it with a ruler so that about the same number of points lie above and below it. It does not need to pass through every point, and it should not simply join the first and last dots. Points far from the line are exceptions, so look for a reason, such as a tributary joining the river or a measurement that was taken badly.
Fieldwork often connects to real issues, such as a plan for new sea defences, a new car park by a river or a flood warning system. Stakeholders will see the same plan in very different ways. Your job is to identify each view, give the reason for it and recognise that people can feel strongly about it.
Likes the plan. More visitors mean more customers and money.
Dislikes the plan. More people may disturb animals and damage plants.
Worried about extra noise and traffic, but might welcome better flood protection.
To deal with a conflict, list who is affected, state what each person wants and why, then compare the views. A compromise, such as a smaller car park with a wildlife area beside it, may satisfy more people. Use questionnaires and interviews to collect views, but remember that a few opinions do not speak for everyone.
Evaluation means reviewing your data and information to decide whether it is accurate and suitable for the purpose, or misleading and unreliable. You met accurate and reliable data in Collecting Fieldwork Data. Now ask more questions.
A conclusion is your final judgement. A strong one does four things.
"My hypothesis that pebbles get smaller along the beach is partly supported. The mean size fell from 60 mm at site 1 to 20 mm at site 5, but site 4 was larger than site 3. This fits with pebbles being worn down as they move. However, I measured only 10 pebbles at each site, so I cannot be fully certain."
A student measured river velocity (in m/s) at six sites: 0.2, 0.4, 0.3, 0.5, 0.4, 0.8. The student read the stopwatch only once at each site.
(a) Calculate the median velocity and the range. [2 marks]
(b) Suggest one way the student could make the data more reliable. [1 mark]
(c) A new car park is planned next to the river. Explain why a cafe owner and a wildlife group might disagree about it. [2 marks]
(a) In order the values are 0.2, 0.3, 0.4, 0.4, 0.5, 0.8. The median is halfway between 0.4 and 0.4, which is 0.4 m/s (1). Range = 0.8 − 0.2 = 0.6 m/s (1).
(b) Repeat each reading several times at every site and take a mean (1).
(c) The cafe owner would want the car park because more visitors would bring more customers (1). The wildlife group might oppose it because more people and cars could disturb animals and damage the river habitat (1).
In part (a) the data is not in order and there are six values, so write the values in order first, then find the halfway point between the two middle ones. Show this working.