Data Sampling and Questionnaires Worksheets | MME

Data Sampling and Questionnaires Worksheets and Revision

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What you need to know

Data Sampling and Questionnaires

Sampling is the process of looking at a small selection of people/objects from a wider population in order to learn new information about that population. For example, suppose you want to know about reading habits in the UK. To do this, you might ask 500 people from the UK how many books they finished last year – this is a sample. In reality, it would be better to ask every single member of the population – then your information is more reliable – but this is often too time-consuming/too expensive to do. The benefit of sampling is that it is less time-consuming, but this also means it might be less reliable, and possibly biased – for example, if you only asked people who were leaving a library, then all your results might be much higher than otherwise. The aim is to make a sample as representative of the whole population as possible (i.e., reduce the amount of bias).

The purpose of a questionnaire is to help extract the information you require, whilst avoiding bias and giving people the opportunity to give a whole range of possible answers. Constructing questionnaires in the correct way and being able to spot poor questionnaires is what you will be tested on. 

Types of Data

Before we go further however, we should know the following 4 definitions.

  • Discrete data (or discrete variables) can only take certain values, e.g. shoe sizes increase in increments of a half: 7, 7.5, 8, 8.5, and so on. You can’t buy size 7.65 shoes.
  • Continuous data (or continuous variables) can take any value, e.g. the height of a person can be any number of centimetres: 182cm, 173.4cm, 167.892cm, and so on.
  • Primary data is data that you collect first-hand, e.g. you go out into the street and ask people how many books they finished last year.
  • Secondary data is data that was collected in the past by other people, e.g. you look at a published survey of 500 people on the internet which asked them about the numbers of books they finished in the previous year.

Revise types of data for a more in depth look and detailed examples. 

Example 1: Sampling Data

A Head teacher wants to determine the popularity of a maths teacher in their school. The maths teacher has classes ranging from year 7 up to and including year 11. It is a large school with over 2000 students and the head teacher doesn’t have time to ask all the students about their thoughts. Suggest a way the Head teacher could collect a sample that represents most of the students in the school?

This is a question that is effectively asking you to avoid bias and collect a representative sample. Bias may come from different year groups having different opinions of the teacher, so for instance the year 7’s may think the teacher sets too much work and is too strict but the year 11’s could think that the teacher is helpful in getting them prepared for their GCSE exams. Therefore the sample needs to cover all year groups, a way of doing this is called stratified sampling. Visit the dedicated stratified sampling page to understand more about this exact method. 

Note: When the population you are sampling is less well categorised than school year groups, often random sampling is the best way to avoid any sort of bias. For instance in biological studies where they want to determine the number of plant species in a large wide open area, they select random spaces to sample by plotting the area on a grid and using a random number generator to select coordinates which tell them which area to sample

Example 2: Questionnaires

Philippa has designed a questionnaire (seen below) to learn about TV-watching habits. She intends to put this questionnaire to 30 of her classmates.

a) Find 2 problems with this questionnaire and explain your answer. 

b) Redesign the questionnaire so that it is more likely to collect meaningful data. 

a) There are actually more than just two problems with this, so we’ll go through them all.

  1. Time Frame – people are asked how many hours of TV they watch, but is this per day, per week, per month? It’s impossible to know without specifying a time frame.
  2. Options – There is no option for someone who watches no TV at all, nor is there an option for someone who watches more than 20 hours of TV
  3. Overlapping options – There is a crossover between the options – if I watch 5 hours of TV, then should I tick the first box or the second? A questionnaire must be clear and easily understandable.
  4. Clarity – It isn’t clear whether or the hours spent watching TV includes time spent watching online streaming services on other types of devices such as phones and computers. 
  5. Bias – Only people from one class are being asked, this doesn’t represent the wider population and ultimately may result in biased data

 

b) Redesigning the questionnaire will mean addressing all of the points listed above. The exact wording in the exam isn’t required to gain the marks, it is making sure you address the logic of data collection correctly and so there is a wide range of answers that will gain full marks. The following questionnaire is an example of one of those answers. 

 

Additionally, there are a couple of other important things to consider when writing questionnaires.

  • Leading questions – questions that include the author’s opinion, e.g. “how amazing was the last Star Wars film?” – this could pressure the person into answering positively, even if they might not agree. They should be avoided, always.
  • Personal questions – questions such as “do you have a criminal record?” might make the person feel uncomfortable and result in a dishonest answer. Knowing this, these types of questions should be avoided wherever possible.

Example Questions

The first criticism is that Tilly’s question is a leading question – she leads people into agreeing with her opinion that the new government will be a disaster.

 

The second criticism is that there are not enough options – somebody might have no opinion on the matter, or they could be neutral about it.

 

Here is an example of an improved question:

 

The first criticism is that there are crossovers between the options – if I spend £30 on food each week I won’t know whether to tick the first or the second box.

 

The second criticism is that there are not enough options – there is no suitable box to tick for someone who spends £150 on food every week.

 

Because he is only asking people at the end of his street, Saru will probably get answers which are lower than if he asked this question at the end of a different street where the houses were bigger/more expensive, therefore his survey will probably be biased.

(a) The first issue with the question is although it does specify the time frame the results will depend on the time of day the person is completing the questionnaire. 

A second issue is overlapping response boxes. Someone who has taken 5000 steps could tick to of the responses. 

(b)

 

Here the question is framed better as is independent of when the form is completed and ask for a value people are more likely to know the answer to on the spot. Also the response boxes no longer overlap. Other improvements could included a response box for those who do not know. 

There needs to be some timeframe referenced in the question otherwise people will answer over varying timeframes. Someone could respond with the amount the receive per week and someone else could give their pocket money amount over the course over year. 

Including a option for zero and having no overlapping response boxes is also important. 

The new questionnaire should look something like: 

 

The original questionnaire has very subjective answer that are qualitative rather than quantitative.

A better questionnaire has the options with a specified number of average visits over a certain timeframe. This will gather much more useful data for the manager of the cinema. 

 

Worksheets and Exam Questions

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Questionnaires and Data - Drill Questions

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Sampling Data and Frequency Polygons - Drill Questions

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