GENERATING A RANDOM SAMPLE WITHOUT TECHNOLOGY

We already know, how to generate random samples by using technology, that is graphing calculator. We can also generate random samples without using technology.

Here, we are going to see, how to generate random samples without using technology.  

Example : 

A tree farm has a 100 acre square field arranged in a 10-by-10 array. The farmer wants to know the average number of trees per acre. Each cell in the table represents an acre. The number in each cell represents the number of trees on that acre. 

How can the farmer choose a random sample of 10 of the acres without technology ?

Solution : 

Step 1 :

To simulate the random selection, number the table columns 1–10 from left to right, and the rows 1–10 from top to bottom.

Step 2 : 

Write the numbers 1–10 on identical pieces of paper.

Place the pieces into a bag.

Step 3 :

Draw one at random, replace it, and draw another. 

Step 4 :

Let the first number represent a table column, and the second represent a row.

For instance, a draw of 2 and then 3 represents the cell in the second column and third row of the table, an acre containing 54 trees.

Repeat this process 9 more times.

Based on your sample, predict the average number of trees per acre. How does your answer compare with the actual mean number, 48.4 ?

Check students’ answers. They may not be very close to the actual mean because the sample was so small.

Compare your answer to the above answer with several of your classmates’ answers. Do they vary a lot ? Is it likely that you can make a valid prediction about the average number of trees per acre ? Explain.

Check students’ answers.

Reflect

Question 1 :

Suppose that you use the method in to collect a random sample of 25 acres. Do you think any resulting prediction would be more or less reliable than your original one? Explain.

Answer :

More reliable; the larger sample should be more representative of the population.

Question 2 :

How could you use technology to select the acres for your sample ?

Answer :

Number the acres in the grid from 1 to 100. Use the formula randInt (1, 100) to generate numbers. Sample the acres with those numbers.

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