Lesson video

Hello, I'm Mrs. Lashley and I'm gonna be working with you as we go through the lesson today.

I'm really hoping you're ready to try your best and make the most of this lesson.

So our learning outcome today is to understand the stages of the Statistical Enquiry Cycle.

The definition of the Statistical Enquiry Cycle is on the screen.

We are going to be working with it heavily during the lesson today.

So you may wish to pause the video and read that before we start.

Otherwise, we're gonna, as I say, build on it as we work through the lesson.

The lesson's got two learning cycles.

The first one, we are really gonna focus on what it is, the Statistical Enquiry Cycle.

And then the second part, we're going to evaluate it and its different parts of it.

So let's make a start on just familiarising ourselves on what the Statistical Enquiry Cycle is.

So when a statistical investigation is to take place, a model of the process can be used.

So the first stage would be to plan the statistical enquiry and ask a question.

And this might be, for example, wanting to find out how often families have a takeaway.

That might be your sort of question that you want to investigate.

And so that would be part of this planning stage.

And next, you're gonna need to collect the data to answer the question that's being investigated.

So if it is about the number of takeaways or how often the families have a takeaway, it might be that you go to a variety of different houses and ask the question.

You might have a survey, you might have a questionnaire and ask them how often they get takeaways.

It might be that you can collect data from a secondary source where you can find out maybe a company that delivers takeaways that you could find out from them.

But you will collect the data in order to try and answer that question.

Then you might organise and present your data.

So if it's, once it's been collected and it might have been collected by you, it may have been collected by somebody else.

So secondary data, you will then present it into some sort of chart or diagram.

So you'll organise it and present it.

Once it's in that diagram and organised, you can do an analysis of it.

So it'd be looking at the diagrams and the charts to see if there's anything significant that pops out and completing some summary statistics.

So you might work out the mean, the median, the mode, the range, and really trying to analyse the data that has been collected.

Once you've done the analysis, we are then thinking about interpretation in the context of your enquiry question.

So if it was about takeaways and how often the people were having it, you would then be having a bit of an idea about the general public's habits when it comes to takeaways and interpreting whether it's more frequent of a weekend and less frequent in the week.

The last part of the cycle or the process, the findings can lead to a more refined enquiry question or actions based on them.

So depending on why you have done this statistical investigation, why were you finding out the habits and how often people were having takeaways? Was it from a health point of view and therefore you're gonna do a a healthy eating campaign? Is it from a company point of view that you want to know how often people are having takeaways and whether it's worth you setting up a takeaway business.

They will give you outcomes.

The refinery process is because it is a cycle.

So it might be that you've decided, okay, I now know it is the weekends that most people are having takeaways.

You might then decide how much money are they spending on takeaways or what type of takeaway, how do they make the decision on the type of takeaway? Is it to do with ratings for the restaurant or cost or delivery times? So you might get to another point where you think, actually this has now led me to further questions.

And so we have a cycle, a more formal model of this is the Statistical Enquiry Cycle.

So our lesson is all about this more formal Statistical Enquiry Cycle, which only has five stages.

So the first stage is planning.

So very similar.

We start by planning what we want to find out, how we're going to do it.

We then collect the data and this is where our six stages has become five.

The organisation, the presentation, and the analysis in the more formal Statistical Enquiry Cycle is one stage and that's called processing and presenting.

So processing the data, which includes the analysis and presenting the data.

Again with charts, diagrams. Then we interpret it in the same way.

So in context of the question.

And lastly, communicating and evaluating.

So communicating the findings in a succinct and easily understood way and also evaluating the process that you went through.

And again, that leads into that refinery moment where you might then go through this cycle again because you realise that you had some flaws in your Statistical Enquiry Cycle the first time.

And so you might want to do it again and try and iron out any of those flaws.

Or it might be that some of the findings has led to a really interesting part that you want to go on and investigate further.

So what does each stage look like and what do you do in each stage? So the planning stage.

It involves defining the question or the hypothesis to investigate, but it also involves deciding what data you're going to collect, how to collect it and how to record it.

So in the planning stage, you really are gonna think about all of the other stages of the process.

Then you'll think about how you're going to process the data that you collect and how you are going to present it.

All of this will happen at the planning stage.

The collecting stage is about gathering the data.

So this could be firsthand, it could be you going out and finding a sample of people and asking questions, but it could be from other sources.

It's considering how data on sensitive subjects may have challenges.

So depending on what your enquiry question, what your hypothesis is, it might be that you need to find data out about sensitive subjects and there are gonna be challenges with that.

So considering how you overcome the challenges of finding out that information.

Then we move to the processing and presenting stage.

So remember this is two from our other process.

In the more formal one, this has become one.

So it involves organising and presenting the data which might need to be cleaned, potentially making use of technology.

So if you was using some sort of spreadsheet software, it's going to struggle to analyse the information if there was characters that is not expected.

So for example, if your question was about time spent watching television and somebody had inputted six hours and had written the word hours, you are gonna have to remove that hours so that the spreadsheet is only working with the digit six.

In the same sense, if the question was about television watching again and somebody else said 30 minutes, you've got an issue of units.

So one person said six hours and we can remove the word hours and somebody said 30 minutes, we can remove the word minutes, but then we've got six and 30.

So you'd have to have made a decision on which unit you're going to use.

So either you're gonna convert the 30 minutes into a half hour or you're gonna turn the six hours into 360 minutes.

So that's part of the cleaning process.

This also involves generating diagrams and charts to represent the data.

And remember back in the planning stage, you would've decided which charts to use.

So is it gonna be a bar chart or a pictogram or a scatter graph or a pie chart? And what would be the best one to relay your information? Then we move on to that fourth stage which is interpreting.

And so what does this involve? Well, it involves analysing the diagrams and the charts and the statistical measures in the context of the problem.

So the stage before you've processed the data, you've cleaned it, you've done some sort of analysis, you've represented it, and now you are going to really think about it in the context of your problem.

It means you're gonna reach conclusions, you're gonna make inferences or predictions related to the starting question or hypothesis.

So going back, remember this is a cycle, why are you doing this? You had a statistical question enquiry or a hypothesis that you were trying to answer.

And so at this stage you are trying to reach conclusions.

It's also here that you're gonna consider the reliability of your findings.

So thinking about whether there could have been any bias, unintentional bias from your sample or other elements that will sort of upset the reliability.

The final stage of the five stage process of the Statistical Enquiry Cycle is communicating and evaluating.

So it involves identifying weakness in the approach or the representations.

So it may be at the planning stage you thought something was the best idea and that was the reason you're doing it.

But after doing it now here you're going to evaluate and identify any weaknesses.

You could suggest improvements to the processes that you went through.

And it involves refining the processes to elicit further information of the initial statistical question or the hypothesis.

So again, there's a process, it's a cycle, Statistical Enquiry Cycle that at this point you might recognise that you could refine it, you could make improvements and go back through the cycle.

So here is a check on this.

Laura is conducting a survey to find out how often people visit the town centre.

Which stage of the Statistical Enquiry Cycle does this event fit in? So pause the video.

You might wanna go back over the last few slides if you're not sure at this point.

But when you're ready to check, press play.

So this is the collecting stage.

She's conducting the survey.

In her planning stage, she would've decided that she was going to conduct a survey and how she was going to conduct it.

But this part in the collecting is when she's actually going out and doing it.

What about Jacob? So Jacob has drawn a pie chart to display his findings.

Which stage of the Statistical Enquiry Cycle is this? Again, press pause and when you're ready to check, press play.

So this is the processing and presenting.

He's presented his findings as a pie chart.

Again, he should have planned that in the planning stage that that's how he would show his findings.

What about this one? Andeep decides that he wants to collect data to help answer the question, how often do adults exercise per week? Which stage of the Statistical Enquiry Cycle does this event fit in? Press pause and when you're ready to check, press play.

So this is the planning.

He's decided that he wants to collect data and that is his statistical question or his enquiry question for his investigation.

So we're onto the first task and the first question is to put the five stages into the Statistical Enquiry Cycle.

So press pause whilst you're putting them into the cycle, think about the order and then when you press play, we'll move to question two.

Question two, I want you to match these events to the stages of the Statistical Enquiry Cycle.

So the events are on the left, the Statistical Enquiry Cycle stages are on the right.

I want you to match them up.

So press pause whilst you're matching and then press play.

We'll move to question three.

Question three, Lucas is investigating whether the length of a film and the age rating have any relationship.

He has planned that he will collect his data from a reliable website.

He takes a sample of films from a variety of age ratings.

What will the next stage of Lucas's investigation be? So consider which stages he's already gone through of the Statistical Enquiry Cycle and what he will have to do next.

Pause the video whilst you are working out that question.

And then when you press play, we'll go to the answers.

So the stages.

The start one at the top.

So we go planning, we plan what we're going to do, how we're going to do it, what data we're gonna collect, what charts we're going to use to present.

Then we go and do the collection, whether that's from a reliable website, whether that's from a survey, a census of data or whether you're actually gonna go out and do that yourself.

Then we move to the processing and presenting stage of the Statistical Enquiry Cycle which follows to the interpreting.

So now you've processed and you've presented it, you're gonna analyse it, consider any limitations, and then moving on to the communicating and evaluating.

And that's where you're really going to focus on if there were any limitations on the processes, whether it can be refined and any sort of outcomes.

And then you might go back through.

Question two you needed to match up.

So there were four events and five stages.

So one of the stages didn't have an event.

So concluding that a new medicine is safe to use would be part of the communicating and evaluating stage.

Asking a group of people their opinion on a new drink would be part of the collecting stage.

Deciding to research the various ways people use their mobile phones is in the planning 'cause you're deciding to research that and using spreadsheet software to analyse the data is in the processing and presenting stage of the Statistical Enquiry Cycle.

And then so we are back to Lucas and his investigation.

So Lucas's next stage is stage three.

The process and present the data and he should use a scatter graph to plot the length of the film against the age rating so he can see if there is any relationship between the two because that's what he wanted to investigate.

So he had already done the planning and the collecting, he was up to the processing and presenting.

Hopefully you got on well with those three questions and you're ready to move on.

So the second part of the lesson, the second learning cycle is evaluating the Statistical Enquiry Cycle.

So let's make a start.

So Andeep wants to investigate whether 15-year-old pupils are eating fruit and vegetables regularly.

He decides to collect some data by asking 10 15 year olds from his school to answer some questions.

So the first question he is asking them is, yesterday, how many portions of fruit or vegetables did you consume? And there are tick box answers, nought, one, two, three, four, five, or more than five.

The second question is, how many days over a week period would you eat at least one portion of fruit or vegetables? And we've got nought up to seven 'cause it's how many days over a week period.

So Andeep flicks through the responses from the 10 pupils and starts to interpret his results.

He concludes that 15 year olds are not eating fruit and vegetables regularly as most of the pupils were not eating at least one portion of fruit or vegetables more than half of the days in a week.

He evaluates his investigation and thinks that he might need to ask more 15 year olds, ask more questions to try and identify how much fruit and or vegetables are being consumed.

So did he follow the Statistical Enquiry Cycle? So just think about what he did.

Maybe look back at the last slide when he decided what he wanted to do and the questions that he was using, has he followed the cycle? So let's just think about each of the stages.

So what did the planning stage look like for Andeep? Well, the planning stage was quite limited, but did have a focus for his investigation.

He considered who he was going to collect, which was his 10 15 year olds and how, and he had two questions.

He didn't decide how to process or represent the data once it was collected.

What did the collecting stage look like for Andeep? So he asked 10 15-year-old pupils from his school.

That's fairly small sample, but it was readily available for him.

So in terms of ease that was readily available.

There were two questions in the questionnaire, both with tick box responses, but we don't really know how Andeep recorded the data collected from the pupils.

We don't know if they all had a copy of the questionnaire and ticked, whether he just went with a clipboard and tallied the amount that he got for each question.

So we don't really know how he recorded it, whether they did it as a whole group and so maybe being influenced by others or whether they did it anonymously in terms of they did it by themselves privately.

So there's all of those factors that really in the planning stage, Andeep should have considered.

So what did the processing and presenting stage look like? Well, he didn't really complete this stage.

So did he follow the Statistical Enquiry Cycle? No, it was at this point that he didn't really follow it.

So he flicked through the 10 responses.

There was a very small sample, but he didn't present the data, he didn't process it.

So he could have looked at the modal response to each question.

So that would be a summary statistic and he could have represented it as a bar chart.

And then he may have seen the modal very clearly, but could also potentially see some sort of shape and distribution.

What did the interpreting stage look like? Well, he did make some conclusions related to his investigation and there is a chance that his conclusions are inaccurate because of skipping the last stage.

So by skipping a stage, there is a chance that you're going to miss a key element of findings.

You might draw false conclusions.

And finally, the last final stage of communicating and evaluating.

He did reflect on his investigation as a whole and made suggestions.

So he suggested he probably needed to ask more 15 year olds.

So his sample of 10 was quite limited.

He also suggested that his enquiry question could be altered or refined to work out how much the 15 year olds are consuming rather than just how regular they are consuming fruits and vegetables.

And therefore he could go back through the cycle again.

So skipping that processing and presenting stage may have led to making false conclusions or potentially missing out on seeing interesting element that could be explored further.

So it's really important that each stage of the Statistical Enquiry Cycle is followed one after the other rather than skipping it, just looking at raw data and making conclusions.

So here's a check.

Lucas says, I'm going to complete an enquiry into teenager's favourite gaming devices.

I will ask my friends what their favourite devices are and jot them down on a piece of paper.

After, I will draw some sort of chart to represent the data and do some analysis.

So what areas of Lucas's plan may need further development? So pause the video and think about this.

There's probably quite a lot you want to say.

And when you're ready to check press play.

He planned to ask his friends.

So it might be that he wants to decide that he knows that he's going to ask and how many.

He might want to develop that a little further.

His data collection sheet, he just said, I'll jot it down on a sheet of paper.

He might wanna actually design a data collection sheet and the questions that he's gonna ask them and decide on the chart.

He said I'll draw some sort of chart.

But he probably wants to decide, that would be a refinement, decide on that chart and any statistical calculations.

So because it is gonna be qualitative data, it's gonna be the types of gaming devices, he's going to use the modal gaming device as a measure of central tendency.

So you are up to your last task of the lesson.

So question one, the first two parts are on this slide and then we move on to C and D.

So Laura is investigating the performance of year 10 pupils and year 11 pupils at sports day.

She's collected data for the javelin event of the distance thrown in metres by the year 10 entries and the year 11 entries.

So you can see them there.

Part A, I want you to comment on Laura's investigation so far.

Is there anything she could have done differently? Can you see anything that she could improve? And then part B, based on the data collected, which year group do you think performed better? So pause the video whilst you're answering part A and part B.

And then when you press play, we'll move on to C and D.

So there's the data again.

Laura wants to know who performed better.

She decides to compare the average distance thrown by year 10 pupils with the average distance thrown by year 11 pupils.

She calculates the mean distance thrown by each group.

She concludes that the year 10 pupils are better than the year 11 pupils.

So part C, do you agree with Laura and justify your answer.

And part D, what should Laura have done differently to reach a more representative conclusion? So pause the video whilst you're working through C and D.

And then when you're ready to move on to question two, press play.

So question two, Izzy wants to know the favourite colour of the pupils in her school.

She asks five of her friends what their favourite colour is and produces this scatter graph to represent her findings.

And her conclusions are purple is the favourite colour.

The darker the colour, the more people have it as their favourite.

So I would like you to comment on each stage of Izzy's statistical enquiry.

Press pause whilst you're doing that.

And then when you're ready for the answers to question one and question two, press play.

So question one, this was Laura investigating the performance of year 10s and year 11s at sports day and she'd collected the distance thrown in metres of their javelin event.

So part A, I wanted you to comment on Laura's investigation so far, thinking about if there's anything she could have done differently and can you see anything that she could improve.

So Laura's investigation is actually fine.

She has planned and she collected the data.

To investigate the full performance of the pupils at sports day, she might want to include more events.

That's something she could do to improve, but ultimately what she's done so far is absolutely fine.

Part B was based on the data collected, which year group do you think performed better? So this is going to depend on how you decided to process the data.

If you calculated the mean, the median, the mode or the range, you should have justified any decision you came to.

So using a summary statistic to compare the two data sets is what I'm hoping you've done, but which one you decided to calculate was up to you.

Then we moved on to C and remember that she concluded that year 10 pupils were better than year 11 using the mean average.

And the question was, did you agree with Laura and justify your answer? And this is all going to be to do with which statistical measure you calculated in part B.

So if you calculated the mean like Laura, then you would agree with Laura because the mean for year 10 was 17.

925 metres, whereas the mean for year 11 was 17.

92375 metres.

So very, very close.

But on average, the mean average year 10 threw further.

If you had used the median, then you would disagree with Laura.

You can see there's quite a difference now between the year 10's median value, median distance thrown and the year 11's.

There isn't a mode on either of the year 10 or 11.

So it's not useful to use that to compare the data sets.

And if we look at the range then you might agree with Laura because there's a more consistent set of results than in year 11.

What should Laura have done differently to reach a more representative conclusion? And this is where seeing the different summary statistics might have helped with part D.

So the mean average is affected by the extreme values.

This meant that the year 11s pupils average was made lower by that 5.

8 metre distance that was thrown.

To compare the average, Laura should have used the median instead because it's not affected by those extreme values.

And when the 5.

87 metre distance is removed, if you consider that as an outlier, the range of year 11 pupils is also smaller than the year 10.

So that one single data value, 5.

87 metres really changes the summary statistics that you calculate for year 11.

If you remove it, if you consider it as an outlier and decide to remove it, then the range gets smaller, they become more consistent as throwers, their mean increases and their median would also increase.

Question two then.

So this was the question you needed to comment on each stage of Izzy's statistical enquiry.

So I'm gonna go through each stage on a different slide.

So the first stage from the Statistical Enquiry Cycle is the planning stage.

So comments that you may have made about the planning stage is that Izzy should have spent more time planning her statistical enquiry.

It was quite limited, she didn't really think about much.

She should have planned more thoroughly who she was going to ask, how she was going to collect it and record the data and how she would process the data after the collection.

So the planning stage is really vital for the Statistical Enquiry Cycle.

It's where you're gonna make all of your decisions about what you're going to do, who you're going to collect it from, thinking about how there'll be limitations, potentially, how you're gonna analyse the data, how you're gonna process it, how you're gonna present it.

Hers was very limited and therefore is one of the reasons the rest of the cycle isn't very good.

Moving on to the collection stage of the Statistical Enquiry Cycle for Izzy.

So she should have asked more than five people and they shouldn't have just been her friends.

So thinking about having a representative sample, we also don't know how she asked her friends, whether they could say any colour.

So could they say royal blue or any colour from the rainbow spectrum? Or whether she had options that they had to select from.

So we are really limited in terms of our understanding of how she collected that data.

Then the processing and presenting stage.

So it would be difficult to apply statistical calculations that are not affected by a small dataset.

So having a very small limited dataset means the statistical summaries might not actually mean too much and there were not two sets of data that might have a relationship with each other.

So the scatter graph was completely the wrong choice of representation.

A pie chart would've been a better choice showing the proportions of choice for each colour.

Then maybe you've commented on the interpreting stage with things like this.

So Izzy concluded that purple was the favourite colour.

The scatter graph had a data plot above each colour.

So one colour was not more favoured than the other.

That conclusion was incorrect.

By her choosing the completely wrong choice of representation, the scatter graph, it wasn't a scatter graph, ultimately, it misled her.

It just made this linear relationship because she just went up one by one as she moved through the colours.

And so then the purple happened to be the highest data point, but there wasn't any more.

All of them had one data point above them, so they were equally favourable.

She also suggested that the darker the colour, the more people have it as their favourite.

And again, she's incorrectly read the scatter graph due to it being the poor choice of diagram.

And lastly, the sample was too small and potentially not representative of all pupils in her school to make a generalisation.

So she's probably over generalised.

Well, she's definitely over generalised based on a very small sample and a misleading diagram.

And then the final stage of the process we know is the communicating and evaluating stage.

So things you may have said on Izzy's statistical enquiry.

A positive, so Izzy's interpretations, although incorrect, were concise.

She didn't blubber on and make a very long paragraph trying to portray her conclusions.

And they were very concise, to the point.

It doesn't seem that Izzy's considered any weaknesses in her processes or considered any changes that may be necessary.

So she didn't really evaluate her process.

So Izzy's statistical enquiry had quite a lot of areas for improvement.

And this is why this last stage is really important in the Statistical Enquiry Cycle.

So changes and improvements can be made and the process will start again.

It's called a cycle because we go through it as many times as we need to, making refinements or finding out further information based on previous findings.

So to summarise today's lesson all about the Statistical Enquiry Cycle, it has five stages.

The formal one has five stages, which is planning, collecting, processing and presenting, interpreting.

And then lastly, communicating and evaluating.

All stages should be completed to ensure that false conclusions are not made.

Really well done today and I look forward to working with you again in the future.