Maximum, minimum, total, range, rank and average
Introduction
Geography draws on a number of different disciplines, including mathematics. Since geography includes numerical information to explain people and places in the world, students need to be able to identify and calculate particular statistics. This chapter explains what maximum, minimum, total, range, rank and average are, and how to calculate each of them.
Statistical data
Geographers collect and examine information from a wide variety of sources. In geography, it is important to not only be able to use visual images such as maps and photographs, but also to be able to interpret statistical data which is commonly presented in the form of tables, graphs and diagrams. Statistical data is numerical information, and is often the result of someone counting or measuring something. It is often organised into a table, so that it can be more easily read and understood.
Below is a table that measures the temperature of a particular place at the same time of day, over a period of five days. This table will be referred to throughout this chapter.
Table 1.
|
Day |
1 |
2 |
3 |
4 |
5 |
Total |
|
Temp (oC) |
21 |
26 |
25 |
33 |
30 |
135 |
See image 1
Maximum and minimum
The maximum is the greatest quantity, degree or value of something. The minimum is the least quantity, degree or value of something. To calculate the maximum of a given set of numbers, students need to locate the relevant statistics and find the greatest amount. In the case of Table 1, the maximum temperature over the five days would be 33oC (Day 4), since 33 is the largest number. If asked to calculate the maximum temperature over the first three days, then the answer would be 26oC (Day 2), since 26oC is greater than 21oC (Day 1) and 25oC (Day 3).
To calculate the minimum of something, students need to locate the relevant statistics and find the least amount. In Table 1, the overall minimum temperature would be 21oC (Day 1). If required to calculate the minimum temperature during the last three days, it would be 25oC (Day 3), since 25oC is less than 33oC (Day 4) and 30oC (Day 5).
Total
The total is the sum of the whole. The total can be calculated by adding a given set of numbers. In Table 1, the total of the five daily temperatures can be found by adding up 21 + 26 + 25 + 33 + 30 = 135. This means that the total temperature is equal to 135oc. If required to find the total temperature of the odd days (Day 1, 3 and 5), then it would equal 76oc, since 21 + 25 + 30 = 76.
See image 2
Range
The range is the difference between the highest and lowest number in a set of given numbers. Range is used to find the spread of a set of a numbers. To calculate the range, the lowest number needs to be subtracted from the highest number. In Table 1, the highest number is 33oC and the lowest number is 21oC. Since 33 - 21 = 12, this means that 12oC is the range of temperatures in Table 1.
Rank
A rank is the positioning of items (statistics) in an ordered sequence (first, second, third etc). To calculate rank, the provided statistics usually need to be rearranged to form an ordered pattern. In the case of Table 1, if the temperatures were to be ranked from highest to lowest, they would appear as follows: 33oC, 30oC, 26oC, 25oC and 21oC. If the temperatures were to be ordered from lowest to highest, then they would appear: 21oC, 25oC, 26oC, 30oC and 33oC.
See image 3
Average
The average (also known as the arithmetic mean) provides the middle value of a given set of numbers. It is not necessarily, however, the middle number when the set of numbers is placed in order of rank. To calculate the average, the set of numbers need to be added to find the total. The total is then divided by how many numbers were added up. In Table 1, the total temperature over the five days equalled 135oC. The average can be calculated by dividing 135 by 5 (the number of days temperatures were recorded). The average overall temperature in Table 1 is 27oC.
If required to calculate the average temperature of the first three days, then 21oC, 26oC and 25oC need to be added together to equal 72. The total of 72 then must be divided by 3 to give the average of 24oC.
