Mathematical Skills » Statistics for Geography: Averages, Trends and Conclusions

Mean, median, mode and range

These four numbers sum up a set of data. The made-up data below are the rainfall (mm) at Station S on seven days: 2, 7, 1, 2, 4, 2, 3.

Key terms:

• Mean: add up all the values, then divide by how many values there are.
• Median: the middle value when the data are put in order.
• Mode: the value that appears most often.
• Range: the highest value minus the lowest value. It shows how spread out the data are.

With an even number of values, the median is halfway between the two middle ones. For 12, 15, 18 and 25, the median is (15 + 18) ÷ 2 = 16.5.

Which one should you use?

An anomaly is a value that does not fit the pattern of the rest.

Relationships between two sets of data

Geographers often ask whether one thing is linked to another. When you describe a relationship, say whether it is positive (both rise together), negative (one rises as the other falls) or whether there is no clear relationship. Always quote figures from the data.

Altitude (m)	100	300	500	700	900
Mean temperature (°C)	14	13	11	10	8

Describing it: there is a negative relationship. As altitude rises, temperature falls, from 14°C at 100 m to 8°C at 900 m, a fall of 6°C over 800 m. The points follow a steady pattern with no anomalies.

Trends over time and the line of best fit

A trend is the general direction data move in over time. Time is always plotted along the bottom (x) axis. The made-up table shows the length of Glacier G, measured every five years.

Year	2000	2005	2010	2015	2020
Length (m)	2,400	2,300	2,150	2,050	1,900

Plot the points as a scatter graph (see Drawing and Reading Graphs). To show the trend, draw a line of best fit:

1. Use a sharp pencil and a ruler.
2. Draw a single straight line through the middle of the points, with about the same number above and below.
3. It does not have to touch every point, or start at zero.
4. Ignore any anomaly when placing the line.

Describing the trend: the glacier got shorter every five years, from 2,400 m in 2000 to 1,900 m in 2020. That is a fall of 500 m in 20 years, or about 25 m a year.

Predictions: interpolating and extrapolating

The further you extrapolate, the less you can trust it. At 25 m a year the line would reach zero length around 2096, but glaciers do not always melt at a steady rate.

Weaknesses and limitations

Statistics can be weak or misleading. Look out for:

• Misleading scales: a bar chart axis that starts at 4.0 t/ha instead of 0 makes yields of 4.1 and 4.3 t/ha look three times different (bars of 0.1 and 0.3), when the real difference is only about 5%.
• Small samples: a sample is the part of a larger group you actually measure or ask. Asking 8 people at one bus stop at 8 am tells you little about a whole town.
• Averages hiding variation: Town P has 60 mm of rain in every season (mean 60 mm, range 0). Town Q has 10, 20, 30 and 180 mm (mean 60 mm, range 170 mm). The means are the same, but Town Q has a flood season and Town P does not.
• Other problems: too short a time period, missing data, anomalies left in, or data from only one place or day.

Drawing and justifying conclusions

A conclusion says what the data show and answers the question. To justify it, use this order:

1. State the pattern or answer clearly.
2. Back it up with figures (a mean, a change, a range, a comparison).
3. Say how far the evidence supports it, and mention any limitation.

Example: "Temperature falls as altitude rises. It drops from 14°C at 100 m to 8°C at 900 m, so the data support the idea that higher places are colder. But there are only five readings, so more data would make the conclusion more reliable."

Designing data collection sheets (accuracy, sample size, control groups, reliability) is taught in Collecting Data for an Investigation.

Exam-style question

Fig. 1.1 shows made-up data for the number of tourists (thousands) visiting Resort R.

Year	2016	2017	2018	2019	2020
Tourists (thousands)	40	44	52	56	63

(a) Calculate the mean number of tourists per year. [2 marks]

(b) State the range of the data. [1 mark]

(c) Predict the number of tourists in 2022, using the trend. [2 marks]

(d) Assess how far the data support the conclusion that tourism in Resort R will keep growing. [6 marks]