TEACHER ENRICHMENT INITIATIVES

Activity 6A: Sampling and Averages

In this activity the students will compare the averages of different sizes of data sets. This will be a multi-step activity. To begin, put the numbers 1-100 on small pieces of paper and place in a hat, box, or small container. These numbers correspond with the participants on the spreadsheet. The students will use the spreadsheet from Lesson 5 for this activity (File Name: “100-entry spreadsheet”). You may also wish to make a copy of the worksheet, “Averages” for each student or one sheet for each group. The students will record what numbers they have drawn to be averaged and the average on this sheet. When the students have completed the averages, instruct them to answer the questions at the bottom. Now divide the class into five groups.
 
  • First Time: Have each group draw two numbers. Instruct the students to go to their spreadsheet and highlight the information that corresponds with these two numbers. The students will now average the two English scores that they have highlighted and record the answer on the worksheet. Have a discussion with the students about their answers. Did any of the groups have answers that seemed strange to them? Why?
  • Second Time: Have each group draw three more numbers. Instruct the students to go to their spreadsheet and highlight the information that corresponds with these numbers. The students will now average all five English scores together; they will use the previously drawn numbers as well. After averaging the numbers, instruct the students to record their answer on the worksheets. Conduct a class discussion about their averages. Is there a large difference between the two averages? If so, why is the difference so large? What affected the averages?
  • Third Time: Have each group draw five more numbers. Instruct the students to go to their spreadsheet and highlight the information that corresponds with these numbers. The students will now average all ten English scores together, they will use the previously drawn numbers as well. After averaging the numbers, instruct the students to record their answers on the worksheets. Conduct a class discussion about their averages. Is there a large difference between the averages? Have the different groups discuss their averages and compare their answers with the other groups. Why are their answers different? Have the averages changed with the increase of numbers averaged together?
  • Fourth Time: Have each group draw ten more numbers. Instruct the students to go to their spreadsheet and highlight the information that corresponds with these numbers. Before averaging these numbers the students will make a tally chart using the twenty English scores. When the students complete their tally sheet of English scores instruct the students to look closely at their information. From this information the students will predict the average of these twenty numbers. Ask the students how they decided on this prediction. Did the tally chart help them make this decision? Instruct the students to record this on the worksheets. Lead the class in a discussion about their averages. The key observation should be that as sample sizes increase, the variability between the averages of the samples decreases. Is their average more or less than the average of all 100 scores? Remind the students of the average, 6.2.You may wish to take your class one step farther, and have the groups average their average together to see if the answer is near 6.2. 
 
After the students have completed their worksheets, instruct them to answer the questions at the bottom of the sheet. Conduct a class discussion using these questions to check for student understanding. Explain to the students that they will not always get the same answer when they conduct sampling activities. The size of the sample will make a difference in the overall results. Ask the students to identify times that they have heard data given to them that is based on sampling. You may wish to bring in the idea of elections and how data is reported out to the public. Ask the students how this data could be incorrect? 
 
Keywords: 

Computer skill, mean, calculation, spreadsheet, cross cultural adaptation, HHIE-S, hearing handicap inventory elderly, sampling, frequency

 

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Activity Code: 
6A
Unit Reference: 
Embracing Diversity
Lesson Reference: 
Lesson 6: Different Sized Samplings