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# Summary on estimation

Topic: Estimation

by Max, 2018 Cohort

Note: This entry was created in 2018, when the task was to “summarise a key reading”, and so may not represent a good example to model current primer entries on.

How many Piano Tuners are there in Chicago? How many gas stations are there in the United States? How many litres of alcohol are consumed in New Zealand each year?

Chances are, you dont know the answer to any of these questions. In fact, if you were to take a random guess in the space of 5 seconds I doubt you would come close at all.

This is where estimation comes in. The Oxford Dictionary defines it as a rough calculation of the value, number, quantity, or extent of something. But what distinguishes estimation from say, a random 5-second guess? Estimation, more specifically, is a calculated, educated guess using a process of logical reasoning. As the initial questions invoke, finding an accurate estimation is often a difficult and complex task.

The complexity of estimation stems from two main concepts:

- It is often difficult to make an accurate estimation in the presence of unknown variables.
- Estimation, unlike conventional guessing, is a process of logical reasoning. There are various methods and processes that can make us better estimators it can be a learnt science.

This primer will discuss one method of estimation, the power of 10 approach. I shall illustrate this method by answering the first question ‘How many gas stations are there in the US?

This method of estimation is a process by which you guess each of the related variables to the question. However, it does not require specific guesses, only guessing to the nearest power of 10.

Before we begin, a ‘power of 10’ refers to the nearest decimal a number falls.

For example, 10^2 = 100, 10^3 = 1000, etc.

Lets start with the first unknown variable what is the US population?

The powers of 10 we have to choose from are:

- 10^7 = 10 million
- 10^8 = 100 million
- 10^9 = 1 billion

Most of you know Australias population is around 20 million, so it is definitely above 10^7. Most people could safely guess the nearest figure to be 10^8.

Now, how many motor vehicles are there in the US?

Our options are:

- 10^1 = (1 car for every 10 people)
- 10^0 = 1 (1 car per 1 person)

Given some people have more than one car, and some dont drive at all, we could take a guess that the closest power of 10 for the ratio of cars to humans is 10^0 (or 1:1).

How often does a typical car get refuelled per week?

- 10^-1 = 1/10 (once every 10 weeks)
- 10^0 = Once per week
- 10^1 = 10 times per week

Lets go with 10^0 = once per week.

Now, how many cars does a typical gas station refuel per week?

Our options:

- 10^2 = 100
- 10^3 = 1,000
- 10^4 = 10,000
- 10^3 (1,000 cars) seems the most accurate.

Thus, we have 10^8 cars in the US, each getting refuelled 10^0 times per week. Each gas station refuels around 10^3 cars per week. Thus, the number of gas stations in the US = 10^8/10^3 = 10^5 (100,000).

The correct number of gas stations is 114,000, so 100,00 is not a bad estimation!

But, are there any problems with this approach?

Yes. This method is fantastic if we can approximate our unknown variables to the nearest power of 10. However, if we miscalculate one of our variables then our final answer becomes much different. For example, if we estimated that instead of 1 car for every 1 US citizen we said 1 for every 10 was more accurate then our answer becomes 10,000 gas stations in the US which is quite far off the correct answer. Alternatively, if we assumed the US population was closer to 1 billion than 100 million then our answer becomes 1 million gas stations. For problem questions that have variables that do not clearly fall within a power of 10, this method is less accurate.

There is no single correct method of estimation to accurately solve every question of approximation, which is why estimation is a complex issue.

#### Disclaimer#

This content has been contributed by a student as part of a learning activity.

If there are inaccuracies, or opportunities for significant improvement on this topic, feedback is welcome on how to improve the resource.

You can improve articles on this topic as a student in "Unravelling Complexity", or by including the amendments in an email to: Chris.Browne@anu.edu.au