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Project Summary

Difficulty	2
Time required	Very Short (a day or less)
Prerequisites	None
Material Availability	Readily available
Cost	Very Low (under $20)
Safety	No hazards

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Sponsored by a generous grant from Motorola

Abstract

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.

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, Concepts and Questions to Start Background Research

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

Materials and Equipment

• measuring spoons
• measuring cups
• glass jars
• dried beans

Experimental Procedure

1. 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.
2. To estimate the number of beans in each jar, you will need to take a sample of beans to use for your estimates.
3. Measure 1 Tablespoon of beans. Count the number of beans in 1 Tablespoon:

4. 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:

5. 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:

6. 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.
7. 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:

8. 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?

Variations

• 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?

• For more science project ideas in this area of science, see Pure Mathematics Project Ideas.

Credits

Sara Agee, Ph.D., Science Buddies

Last edit date: 2006-01-19 17:48:00

Career Focus

If you like this project, you might enjoy exploring careers in Pure Mathematics.

	Mathematician 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.			Statistician Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician!
	Math Teacher Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime!			Economist Every country has resources—people, land, raw materials, capital, and machinery—and economists study how those resources are distributed to create the goods that people buy, and the services people need or want. In their studies, economists monitor economic trends and collect data on things like energy costs, inflation, interest rates, exchange rates, business cycles, taxes, and employment levels. Based on their analysis of this data, they develop forecasts of economic activity so that businesses and governments can better plan for the future.

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