Pupil Poll Statistics In Your World 
Student Notes
Teachers Notes
Selecting the People to Ask
 
What a Poor Choice!
 
Who's in the Queue?
 
Four from the class
 
Who Will Represent the School
 
Some from Each Year
 
Which Is the Better Sample?
 
What Are the Favourite Albums?
 

Good Samples, Bad Samples and the Poll

Selecting the People to Ask
In our poll for the record album library, you will have to decide which pupils to ask.

  1. Write down the disadvantages of asking all the pupils in the school. Write down one advantage in asking only a sample.
  2. How will you select a sample of pupils?

The sample should be representative of the school. Every pupil should have the same chance of being chosen.

  1. Copy down each method below. Write down whether it is fair. Give your reasons. Only two of the methods are sure to be fair. The first one has been done for you.

Choose in your class only.
Unfair beciuse no other class has a chance of being asked.

Choose 50 pupils in the playground.

Take a school list and choose every 10th pupil

Choose 50 pupils from your year group.

Take the first 50 replies to questions in the school magaazine

Ask four pupils from each class in the school.

Announce the poll in assembly and ask the first 50 pupils who volunteer.

Ask 1 in every 10 pupils from each year group.

Ask five pupils as they come into school

Invite pupils to attend i meeting and ask those who attend.

 

What a Poor Choice!
Below there are some examples where the sample was not well chosen.

Remember that a sample should be representative.

  1. Copy down each example and try to say whether it is a bad sample. The first one has been done for you.

Only people who stopped at motorway cafes wereasked about the quality of the food.
(This is not a representative sample. Those who think the quality is bad may not stop. You should try, to ask a sample of drivers who use a motorway)

People with telephones were phoned and asked how they intended to vote.
A Scottish newspaper invited readers to write in about
devolution to find whether people wanted separate government for Scotland.
A reporter asked five pupils what they thought about the school leaving age, and said 80% of puplis wanted it lowered.
People outside a post office on a Tuesday were asked about nursery schools and playgroups. (Hint: Family allowances are payable at post offices on -Tuesdays.)
The first 10 people off a bus in the rush hour were asked about bus sevices in the town.
An interwiewerwent to 50 houses during the day to ask about the quality of faishionable clothes for teenagers.

 

Who's in the Queue?
An interviewer asked people at bus stop about bus travel.

  1. Use the picture to help you explain why he may not get a representative sample.

Four from the Class
Suppose you Want to choose four pupils from you class. How can you do this fairly?

Here are two ways:
Each puipil wriites his or her name on a piece of paper.
T he names are put in a box.
Choose four from the box.

Number each pupil. Then read two-digit from a random number table.

  1. Using the second method, what would you do if you got the same number twice?
  2. Are both methods fair? I'se one method to select four pupils.

You want to select a simple of pupils from the whole school.

  1. Which method would you use? why?

 

Who Will Represent the School?
You are going to use a fair method to select a sample of pupils from the school. The sample should be representative of the school. You will need a list of the 'Pupils you want to survey. You will choose a sample of pupils. Your teacher will guide you. We consider two methods.

The first method gives a SIMPLE RANDOM SAMPLE. every pupil has the same chance of being chosen.

  1. Give each pupil a number startin at 001. Does the order in which the pupils are numbered matter?
  2. Read three-digit numbers from a random number table until you have chosen 50 different pupils.
  3. Write down the names a nd years of pupils you have chosen. This is your random sample.

You have used a fair method to select a random sample. We want to know if' the sample is representative. You can use Table 4 on pige R1 to help you answer this.

  1. Fill in the numbers of pupils in each year of the school in the second column of Table 4.
  2. Count the numbers of pupils in each year in your sample. Put these numbers in the fifth column of the table headed 'Random Sample Size'.
  3. Is each group reasonably represented?

Suppose your random sample contained only pupils from the first year.

  1. What would you do?

One answer is given in Section C6.

 

Some from Each Year
Pupils of different ages may, have different favourite albums. You may want to be sure each age is fairly, represented. To do this we choose a STRATIFIED SAMPLE.

One way to do this would he to select 10 pupils from each year group.

  1. Why might this be unfair?

Table 1 shows the number of pupils in each year at Logsvllle Comprehensive School. There are 602 pupils altogether in the five years.

Year Number of pupils Calculation Stratified sample size
1 94 50/602 x 94 = 7.8 8
2 86 50/602 x 86 = 7.1 7
3 147 50/602 x 147 = 12.2 12
4 159 50/602 x 159 = 13.2 13
5 116 50/602 x 116 = 9.6 10
Total 602   50

Table 1 - Pupils at Logsville Conprehensive School

We want to choose a sample of size 50 out of 602. This is 50/602 of the pupils.

To be fair we should choose this fraction of each year. In year 1 there are 94 pupils. 50/602 of 94 is 7.8. This number is in column 3 of Table 1.

We can only choose a whole number of pupils so we choose the nearest whole number to 7.8, which is 8. This number is put in column 4. The figures for the other four vears are worked out in the same way.

Complete Table 4 on page R1 as follows:

  1. Fill in the total number of pupils.
  2. Write down 50 as a fraction of the total number of pupils.
  3. Work out this fraction of the number of pupils in each year. Write your answer in column 3.
  4. Write these to the nearest whole number in column 4.
  5. Check that the total sample size is 50 (or very near to 50).
    Why might it not be exactly 50?

Your Table 4 now shows how many, pupils to choose from each year to give a stratified sample.

  1. Use random numbers to select pupils from your list for this stratified sample. Write down the names and forms of the pupils you have chosen.

 

*Which Is the Better Sample?
Using Table 4:

  1. Draw a bar chart showing the numbers of pupils in each year group in the school.
  2. Draw a bar chart to show how many pupils were selected from each year in the random sample (the first one).
  3. Draw a bar chart to show your stratified sample(the second one).
  4. Which is the more representative sample?

 

What Are the Favourite Albums?
Your teacher will help you through this section.

  1. Decide on the sample of pupils you will ask.
  2. Make a list of the top 30 albums.
  3. Ask the pupils in your chosen sample to choose their five favourite albums from your list. Put tally marks against the list.
  4. Count the votes for each album.
  5. Put the albums in the order of the votes cast.
  6. Write a report on your opinion poll. You should include in your report a few sentences on each of the following:
    • The purpose of the poll.
    • How you selected the sample.
    • What questions you asked.
    • How you drew up the list of albums.
    • What problems you met in questioning the pupils, e.g. absentees, pupils did not understand the
      questions.
    • How you overcame these problems.
    • How you analysed all the results.
    • Whether the sample was a good one (i.e. representative).
    • Whether the poll could be improved, if so how.
    • What you think the five most popular albums in the school are.

 

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