Collecting Data
Text Reference: Pages 206-207:
Read the following. Take particular note of the difference between the terms Census and Sample
Random Sampling vs Systematic Sampling:
Class Activity #1: For this activity you will be required to use Excel. You will be given a copy of the spreadsheet Age at First Flight in a Plane. On this you will see data for 180 passengers. We will use Excel initially to generate a set of random numbers that we will need to enable us to select the passengers to sample. Open Excel and immediately save your spreadsheet as RandomNumber.
What are random numbers: Random numbers are numbers that are generated between set limits so that there is no pattern or bias in the way that they are chosen. You might think that it is easy to choose numbers at random just by thinking of the first number that comes into your head. This is, however, not the case. Thus mathematical techniques have been developed that allow the selection of numbers with no bias. That is no number is chosen in preference to another number. The formula in Excel that allows you to choose such numbers is
=RANDBETWEEN()
Inside the parentheses you type the range from which you wish the numbers to be chosen. In this case you would type the following.
=RANDBETWEEN(1,180)
You will notice that this will choose numbers between 1 and 180 INCLUSIVE. That is, it will include the possibility of choosing a 1 or a 180. Set up your spreadsheet so that it looks similar to the following.
Into cell A3 type the formula as shown below.
Now copy this formula across to column I, as shown below.
You now have a set of nine (9) random numbers. Write these numbers down on your Age at First Flight in a Plane sheet. If you have two numbers the same add one to the number and provided it is not a duplicate use that value. These numbers represent those passengers that you will select for your sample. With a pen circle those passengers on the sheet.
The easiest way to analyse your data is to set up a spreadsheet with this data copied onto it. See below.
To calculate the mode, median and mean use appropriate Excel formulas. An example is shown below.
Let us now try the whole process again. From the FORMULA menu in Excel click the CALCULATE NOW icon. See below,
This will generate a new set of random numbers. Select these passengers on yourAge of First Flight sheetand then transfer this new set of passenger data to the spreadsheet as shown below.
Calculate the mode, median and mean again.
Q1) Comment on the differences and similarities you found between the two sets of data. Write your answer into your workbook.
Class Activity #2: For this part we will be using a systematic sample. To do this read the following which comes from your text.
Of course you will record all of this data on your spreadsheet. See below.
In a similar fashion calculate the mode, median and mean.
Q2) Write a sentence in your workbook comparing the two techniques.
Class Activity #3 – Extension: If you reach this point you will analyse the entire data set. This is in fact the same as analysing the data from a census. To do this you will need to download the spreadsheetFirstFlightNoFormulas. This form of the data has had the formulas removed and is just a set of numbers. Calculate the mode, median and mean.
Q3) How do the results obtained from using all of the data, a census, compare with the random sampling and systematic sampling?
You will notice that another column has been added to this spreadsheet. This is the RandomAgecolumn. Each time you press the CALCULATE NOW button a new set of data is generated randomly. The ages are random between the limits of 5 and 13. Calculate the mode, median and mean for this set of data and compare what happens to this set of data each time you press the CALCULATE NOW BUTTON.
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Age of First Flight in a PlanePage 1