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Sampling And Bias | A Level Statistics Success

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Introduction

If you need to obtain information from a small group of people then you can survey all people involved. 

However if you require information from a much larger population then it will not be possible to survey everyone. In such cases a sample of the population will be sufficient. 

In order to make the data meaningful the data needs to be large enough otherwise it could be biased data. 

For example: If you are presented with the questions “Girls are more intelligent than boys” then you would need to ask an equal amount of girls and boys this question. Asking too many boys or too many girls will make the data biased. 

Sampling And Bias - Types

There are essentially two types of sampling: 

  • Random here every member of the population has an equal chance of being chosen


Stratified here the population is divided into smaller categories and the number of members in each category is calculated. You then need to ensure that the calculations are done in the same proportion as in the entire population i.e \frac{\text { sample size }}{\text { total population }}

Sampling and Bias - Stratified Sampling

Example: 

In a school a sample of 50 students is needed for a survey. The school is divided into three years as shown below:

\begin{array}{|c|c|c|} \hline \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\ \hline 327 & 246 & 401 \\ \hline \end{array}

How many students from each year should the teacher ask?

Solution: 

This is a typical example of a stratified sampling question as the school as a whole has been broken down into categories. 

In order to find the number of students we first need to find the size of the total population: 327 + 246 + 401 = 974

In order to find the number of students from each year we multiply \begin{gathered} 50 \\ \hline 974 \end{gathered} by the size of each category. 

Year 1:

327 \times \frac{50}{974}=17

Year 2: 

246 \times \frac{50}{974}=13

Year 3: 

401 \times \frac{50}{974}=20

Remember:

  • Always round up numbers
  • Find the sample by multiplying each group by \frac{\text { sample size }}{\text { total population }}
  • Make sure the numbers add up to the correct sample size
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Multiple Choice Questions

  1. You are researching the price of train tickets. You ask ten people who are stood at the platform at 10am the cost of their tickets. What is wrong with this?

    1.  Sample is too large and takes place all day
    2.  Sample is too small and can only ask at 10am
    3.  Sample is too small  
    4. Sample is perfect

     

    You are looking into shopping habits of people. You interview 25 women on a Wednesday morning. What is wrong with this?

    1.  Asks only women and only done once
    2.  Asks only women 
    3.  Only done once  
    4. Best results would be Wednesday afternoon 

     

    You are asked “children watch more TV than adults”. You ask 5 boys and 5 teachers what they watch. What is wrong with this?

    1. Sample too small
    2. Only boys asked  
    3.  Sample too small and only boys asked 
    4. Sample of ten is too large

     

    You are asked “men watch more football than women”. How could you test this?

    1.  Only ask men in different locations, of different ages and at different times
    2.   Ask equal number of men and women, different ages, different locations, various times. 
    3.  Only ask women in different locations, of different ages and at different times
    4. Send letters to all males and females in the country and to ask for a response. 

     

    Is a postal survey effective?

    1.  Yes but the internet is better
    2.   Everyone might not respond or reply back at different stages
    3.   Only in a local area
    4. Only if a free post envelope is provided

     

     It is suggested that more girls go to church than boys. You do a survey in church on Sunday and count the number of girls. Is this suitable?

    1.  Yes church is open on Sunday
    2.  Yes church is only open on a Sunday
    3.  No. Church is not just open on a Sunday. 
    4. Yes because everyone will attend on a regular basis

     

    A group of people asked for a zebra crossing on a busy road. The council performed a survey asking 100 people. Is this suitable?

    1.  No. Too small a sample
    2.  Yes – sample is suitable 
    3.  No – sample too large
    4. No because you don’t know how many cars travel on the road

     

    You are conducting research about smoking in public and you ask 50 non-smokers. Is this suitable?

    1. Yes  
    2. No  – sample too large  
    3. No. Data is biased
    4. Sample is ok but the data is biased

     

    You are conducting a survey about those who own a DVD outside a DVD store. Is this suitable?

    1.  Yes – they all own a DVD
    2.   No. Data is biased
    3.   No – sample size unknown 
    4. Not clear if asking males or females

     

     You want to know the most popular type of car in the UK and so you visit the local car park and sample the first 100 cars. Is this suitable?

    1. Yes – gives a good idea of what people own across the UK
    2. No – sample too large 
    3. No sample is too small for whole of UK
    4. It would be best to count the first 100 cars on the road rather than in a car park 

      Answers:

    1 – b; 2 – a; 3 – c; 4 – b; 5 – b; 6 – c; 7 – a; 8 – c; 9 – b; 10 – c

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