# Estimation and Population Size

Difficulty | |

Time Required | Very Short (≤ 1 day) |

Prerequisites | None |

Material Availability | Readily available |

Cost | Very Low (under $20) |

Safety | No hazards |

## Abstract

Have you ever wanted to take a short cut? How about when doing your math homework? In this experiment you can learn how estimation can save you time doing math calculations. But beware, some estimations are better than others! Can you match this sample size with the best population? How accurate are your estimation skills?## Objective

In this experiment you will estimate the number of beans in small, medium, and large populations to test if estimates are more accurate for small or large populations.## Share your story with Science Buddies!

Yes, I Did This Project! Please log in (or create a free account) to let us know how things went.## Credits

## Cite This Page

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.### MLA Style

*Science Buddies*, 28 July 2017, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p014/pure-mathematics/estimation-and-population-size. Accessed 15 Nov. 2018.

### APA Style

*Estimation and Population Size.*Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p014/pure-mathematics/estimation-and-population-size

Last edit date: 2017-07-28

## Introduction

Sometimes, everyone wants to take a short cut to get the job done. Sometimes a shortcut can be a bad thing, but sometimes it can save you a lot of time and come pretty close to doing a good job. One time-saving shortcut when dealing with numbers is estimation. Estimation allows you to do a complex calculation more quickly, and can be useful when a quick answer is more important than an accurate answer.

Accuracy is how close a measurement or calculation is to the actual value. When making an estimate, it is good to have an answer that is as accurate as possible. What if you are doing an estimate of how much money you will need to bring to the store? An accurate estimation will leave you with enough money to buy what you need, but an inaccurate estimation might leave you at the cash register without enough money!

How can you make an accurate estimation? One way is to match the size of the sample with the size of the population. A sample is a small portion of what you are calculating that you use to make your estimation. A sample is supposed to represent a model of the entire population, or group. To get an accurate estimate, it is important that the size of the sample fit the size of the entire group. It can't be too small or too large, but just right.

In this experiment, we will try to get a good estimate of the number of beans in a jar. We will use three different population sizes, small, medium, and large. Will our sample size be a good fit for one of these groups? Which group will our sample give the best estimate for?

## Terms and Concepts

To do this type of experiment you should know what the following terms mean. Have an adult help you search the Internet, or take you to your local library to find out more!- estimate
- multiplication
- division
- subtraction
- sample
- calculation
- error
- accuracy

## Bibliography

- Sohn, Emily. 2005. "Wired for Math." Washington, D.C. Science News for Kids. 12/30/05.

http://www.sciencenewsforkids.org/articles/20051207/Feature1.asp

## News Feed on This Topic

*Note:*A computerized matching algorithm suggests the above articles. It's not as smart as you are, and it may occasionally give humorous, ridiculous, or even annoying results! Learn more about the News Feed

## Materials and Equipment

- measuring spoons
- measuring cups
- glass jars
- dried beans

Estimation and Population Size

#### www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p014/pure-mathematics/estimation-and-population-size

## Experimental Procedure

- Fill three glass jars with three different measures of dried beans: small (1/2 cup), medium (one cup), and large (two cups). These will be your three different populations that you will make an estimate for.
- To estimate the number of beans in each jar, you will need to take a sample of beans to use for your estimates.
- Measure 1 Tablespoon of beans. Count the number of beans in 1 Tablespoon:
- Now you need to calculate the number of Tablespoons of beans in each of your jars. If there are 8 Tablespoons in 1 cup, how many Tablespoons are in half of a cup? Divide 8 by 2 to get your answer. How many Tablespoons in 2 cups? Multiply 8 by 2 to get your answer:
- Now you are ready to make your estimates by multiplying the number of beans you counted in 1 Tablespoon by the number of Tablespoons in 1/2 cup, 1 cup, or 2 cups:
- Now comes the hard part! You need to open the jars and actually count the beans so that we can calculate how accurate our estimates were. Open each jar, count the number of beans inside and put the data in this data table below.
- Last, we need to calculate which estimate had the largest error, the small population (1/2 cup), the medium population (1 cup), or the large population (2 cups). We are going to do this in a very simplified way, we will calculate the difference in number between the estimate and the actual counted number of beans by subtracting:
- Compare the error of the small, medium and large populations. Which group had the estimate with the least error? Which group had the estimate with the largest error? Can you think of a way to minimize the error, or make a better estimate?

## If you like this project, you might enjoy exploring these related careers:

### Economist

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Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more### Math Teacher

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- Another way to change this variable is to have one population of beans that you wish to estimate (2 cups), and to take multiple sample sizes (1T, 2T, 3T). The calculations for this method are slightly different from the experiment above, can you figure them out? How does the accuracy of these estimates compare?

## Share your story with Science Buddies!

Yes, I Did This Project! Please log in (or create a free account) to let us know how things went.## Ask an Expert

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