Estimation and Population Size
|Time Required||Very Short (≤ 1 day)|
|Material Availability||Readily available|
|Cost||Very Low (under $20)|
AbstractHave 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?
ObjectiveIn 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.
Cite This PageGeneral 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.
Last edit date: 2017-07-28
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 ConceptsTo 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!
- Sohn, Emily. 2005. "Wired for Math." Washington, D.C. Science News for Kids. 12/30/05.
News Feed on This Topic
Materials and Equipment
- measuring spoons
- measuring cups
- glass jars
- dried beans
Remember Your Display Board Supplies
Poster Making Kit
ArtSkills Trifold with Header
- 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?
Communicating Your Results: Start Planning Your Display BoardCreate an award-winning display board with tips and design ideas from the experts at ArtSkills.
If you like this project, you might enjoy exploring these related careers:
EconomistEvery 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. Read more
ActuaryLife is full of risks to both people and property. Actuaries predict the chances that future negative events will occur in a person's life, and then think of ways to reduce those chances, or reduce the impact of those negative events. Actuaries help bring peace of mind to both families and to businesses. Read more
MathematicianMathematicians 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 TeacherMath 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! Read more
- 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?
Ask an ExpertThe Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.
Ask an Expert
News Feed on This Topic
Looking for more science fun?
Try one of our science activities for quick, anytime science explorations. The perfect thing to liven up a rainy day, school vacation, or moment of boredom.Find an Activity