George Bott
  This is a stand-alone project.

  Adult basic education, Critical thinking, Problem solving, Job skills, Life skills, Mathematics

Learner Level:
  All levels

Time Frame:
  All work can be completed in two 4-hour class sessions.

Learner Grouping:
  Small group, Whole class

  This class is attended by four or five students and meets four hours a day for five mornings a week. Learners are a combination of those who attend through Fresh Start and those required to attend the class in order to keep their welfare benefits, but attendance is still sporadic. The regular classroom equipped with tables rather than desks is used for most sessions. For this learning activity, planning and data analysis was done in the classroom. The data gathering was done in the field.


Type of Program:

Student Population Served:
  Select population

Statistical sampling

Learners collect data in the field and analyze it in class using tables and graphs to determine how many observations of a phenomenon are necessary in order to draw reasonably valid conclusions about it. Learners discover the power of statistical sampling in searching for information. __________________________________________________________

Learning Objective:

  • Learners will analyze a problem situation to determine the need for data.
  • Learners will plan how to obtain and organize data needed.
  • Learners will analyze data and draw conclusions.
  • Learners will write a report on their project.

Primary Skill:
Learn through research

Secondary Skills:
Plan, Observe critically, Use math to solve problems, Reflect and evaluate, Convey ideas in writing

Learner Needs & Goals:
Learners realized they needed more information about the loss of business when discussing why a local restaurant had closed. This led to a discussion about data gathering and the use of data in drawing conclusions. I designed this project to provide experience and practice in data collection along with an understanding of how much data to collect.

Learning Activity Description:
For this project, I decided to ask the class to determine the ratio of each of the following types of vehicles traveling along a busy interstate near our classroom: cars, mini-vans, SUVs, and pickup trucks. If there are enough learners to do the activity, it could be expanded to find the ratio of vehicles of a certain color, etc. Actual data taking would be done at a safe location along the highway but at a position close enough to permit learners to recognize the selected vehicles. I chose a location on a dead-end access road that has a good view of the highway. I avoided a location within the city limits since that location might have involved double counting as vehicles return in the other direction after a short shopping trip.

This learning activity has four parts: preliminary discussion of the activity, data collection, analysis and presentation of data, and writing a report describing the activity.

Preliminary discussion of the activity

  1. Lead a class discussion on the loss of business at a restaurant and what could be done about it. Have the learners brainstorm a list of reasons for the loss.

  2. Discuss the possible relevance and importance of each item on the list. (NOTE: The class will suggest that a consumer survey should be conducted.)

  3. Discuss how to do a consumer survey so that the data obtained will be relevant and unbiased.

  4. A discussion of  how many consumers have to be surveyed usually leads directly to the issue of sample size.

  5. Since a consumer survey would be difficult to conduct, suggest that a vehicle survey would provide the same experience in collecting data.

    Tell the class that they should select types of vehicles traveling on I-40; for example, cars, minivans, SUVs, and pickup trucks. Explain that they will take counts of each type of vehicle in 5-minute intervals and that data sheets will be required.

Data collection

  1. Have the class  construct the Data Gathering sheet and describe how the data will be taken (who will do what, etc.). For clarity, call this Sheet 1. Sheet 1 will have 5 columns. On the left should be the column for listing the number of the 5-minute intervals. (Numbered in advance from 1 to 24 would hold two hours worth of data.) The next four columns, a, b, c, and d, would be the place to tally each of the vehicle types in each 5-minute interval. Column "a" would be for cars, column "b" for minivans, and column "c" for SUVs, and column "d" for pickups. When Sheet 1 has been completed, cell 1a would contain the tallies of the number of cars that passed the checkpoint during the first 5-minute time period. In like fashion, cell 24d would be the tallies of the number of pickups that passed the checkpoint during the last 5-minute time period. (See the example of sheet 1 below.)

  2. Having explained all the above, and having prepared the data-gathering sheet, it is now time to take the class to the "field" to collect data. Place the learners into groups of three. Each group needs the data-gathering sheet, a clipboard, a watch, and a couple of pencils. Duplication of data taking is OK and can lead to a bit of rivalry in analysis and results. One learner in each group should be the data taker tallying the number of vehicles of each description in the correct cell as they are called out. The second learner is the timekeeper, calling out the five-minute intervals. The third person is the vehicle observer calling out the identity of vehicles as they pass. The observer must be one who knows how to identify the different types of vehicles correctly.
  3. Here is a sample of a completed data sheet:

    Note: Collecting data is tedious work and gets somewhat boring. A nice reward is a stop at Burger King or McDonalds on the way back to the classroom.

Analysis and presentation of data
Analysis of the data will require one sheet of graph paper and the preparation of two additional data sheets. Data Sheet 2 will show the cumulative totals by time period of each type of vehicle as well as the cumulative total of all vehicles by time period. Data sheet 3 will show the ratio of the cumulative counts on Sheet 2 to the row total count in column e. of Sheet 2.

  1. Have learners prepare Sheet 2. It will be the same as Sheet 1, however, Column e. is added for the total number of vehicles per time period. Learners must collect the data on each vehicle per time period from each group and then tally the total number of counted vehicles per time period. (See a sample of the completed Sheet 2 below.)

  2. Sheet 3 will be the same as Sheet 2. The 5-minute intervals will be the same as before. The entry in columns, a.-d. will be the ratio of cumulative counts to the row total count in column e. (all numbers taken from Sheet 2). Then for comparative purposes, the ratio will be changed to decimal fraction. A calculator may be used. Again using the above sample data, Sheet 3 when completed would look like this:

    Thus, after 30 minutes (time period 6), the total number of pickups that had passed the checkpoint (using this sample data) was 15 and the ratio of pickups to total vehicles after 30 minutes was 15 out of 103 or .15 (15%).

  3. The ratios computed on sheet 3 should be plotted on the graph paper with 5-minute interval on the abscissa, and ratio on the ordinate. A unique symbol should be used for the ratios of each vehicle type. The ratios for each vehicle type will likely jump around a bit for the first few 5-minute intervals, but should then begin to settle down to a fairly straight horizontal line for the later 5-minute intervals. The 5-minute interval at which the ratio settles down to (or near) the straight line is the approximate desired time required for taking data.

  4. After the graphs are finished, ask each group to tell how many 5-minute intervals would have been sufficient to get reasonably accurate estimates of the true ratios. Discuss what is meant by "reasonably accurate". Would, for example, "reasonably accurate" be the same in quality control of medicinal drugs or of dimensions of ball bearings as it would be for a vehicle count? What is "reasonably accurate" will be different in different fields, or even in the same field depending on the purpose for which the results are to be used.

Writing the report
Following the data analysis, each learner is asked to write a report detailing the problem researched, the methods used to gather data, and the results of the study.

The writing assignment, the report of how this problem was researched, will show whether or not the learners understood what they did. Learners should be able explain how to run an experiment to determine what fraction of cars on the highway are driven by men who wear hats. They should be able to tell (after the fact) how many 5-minute intervals of observations are required to make a reasonably accurate estimate of this fraction. To determine if the learners can generalize to other problems, a different sort of problem could be presented for class discussion to see how learners would go about solving it and delimiting the amount of data needed.

I have no reflections since I have not done this one yet. It is a warm weather activity and I expect to do it soon.


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