Lesson video

This lesson is continuous variation: data handling and analysis from the unit variation differences within species.

Hi there.

My name's Mrs. McCready and I'm here to guide you through today's lesson.

Thank you very much for joining me.

I hope you're looking forward to today's lesson.

Now, in today's lesson, we're going to look at data from continuous variation and plot it as a histogram before going on to have a look at possible causes of that variation.

Now, we're going to come across a good number of keywords in today's lesson, and they're listed up there on the screen now.

You may wish to pause the video and make a note of them, but I will introduce them to you as we go, so there's not absolutely any need for doing that.

And in our lesson today, we're going to have a look at plotting continuous data before we then go on and analyse and draw some conclusions from it.

So are you ready to go? I certainly am.

Let's start.

So we know that there is great variation between individuals within a species.

Looking at the apples there on the screen, we can see that there is great variation between each one of them.

Each of them will have a different mass, for instance.

Now, this type of variation is called continuous variation because there are a great number of numerical values present within an acceptable range.

And any value involving length or mass is going to be continuous.

Now, continuous data may take any one of many, many values, possibly infinite values within a continuous range.

So what is continuous variation? Is it A, variation which is categorical, divided into particular categories? Is it B, variation which happens all of the time? Or is it C, variation which can take any one of many values over a continuous range? I'll give you five seconds to think about it.

Okay.

Have you decided? So hopefully you've chosen the last option there.

Variation can take any one of many values over a continuous range as your definition for continuous variation.

Well done.

So when you observe continuous variation, it gives a spread of data across a continuous range.

So let's have a look at some year eight data, for instance.

The heights of some year eight students.

We can see that there is a range of data from the shortest student being 136 centimetres high to the tallest student being 161 centimetres.

Now, if we measured more students, let's say we measured 100 year eight students, we would get many more values, many of which would be within that range of 136 to 161 centimetres.

And we may also get some shorter students and some taller students besides.

We could also measure those students to even greater precision.

So for instance, we could measure down to the nearest millimetre and that would give us even more values and very unlikely that we'd have any student being precisely the same height if we went down to that level of detail.

However, when we look at data like this, it's quite tricky to see patterns which are present within the data.

So sometimes it's easy to group that data into ranges and that might help us see those patterns more clearly.

So if we take those five students, for instance, we could group them into heights of between 130 and 139 centimetres, 140 and 149 centimetres, 150 and 159 centimetres and so on.

So let's have a go at doing that now.

So we can see that there are two students who have a height between 130 and 139 centimetres.

We have two students who have a height of between 140 and 149 centimetres.

There are no students within 150 and 159 centimetres.

One student between 160 and 169 centimetres and no students of 170 to 179 centimetres.

So straightaway, we've got a little bit more information there which might make it easier to interpret.

So have a go at grouping this data into ranges.

So you might wish to pause the video and come back to me when you're ready.

Okay, so have you seen that there are no students between 130 and 139 centimetres? There is one student between 140 and 149 centimetres, three between 150 and 159, two between 160 and 169 and one between 170 and 179 centimetres.

Well done if you did.

If we have a huge amount of data, we can plot the ranges and their frequencies as a graph to make it easier to see trends and patterns.

So we could plot that data as a histogram, for instance.

And you can see that in the histogram there, we have the data in ranges with their frequencies plotted as columns that touch each other.

And it's very important that those columns fall in a particular order, that they go 110, 120, 130, 140, 50, 60 and so on.

Now, a histogram is different from a bar chart and it's worth making sure that you understand the difference between a histogram and a bar chart.

So a histogram is displaying continuous data and that data is grouped into ranges, which is why there's columns being shown as opposed to dots.

And those columns touch each other and are present in a very particular order.

So they are the three key features that you would be looking for if you were plotting your data as a histogram.

Continuous data in ranges with columns that touch.

Compare that then to a bar chart.

So a bar chart is displaying discontinuous data and therefore, the data is in categories.

And because the data is in categories, the columns do not touch.

And actually, it doesn't really matter which order those columns go in, they could go in any order, although some order might make it slightly more easy to interpret the data, but it is not fundamental to the interpretation and it certainly won't alter the interpretation if the columns are put in a different order.

So those are the features for a bar chart.

Discontinuous data, therefore categorical data where the columns are separate and do not touch.

So let's have a review of that.

Can you use those four words to fill in the gaps? A histogram displays something data in something plotted as columns that touch and a bar chart displays something data in something plotted as columns that do not touch.

Have a look, see what you think and come back to me when you're ready.

Okay, so let's have a look.

A histogram displays continuous data in ranges plotted as columns that touch and a bar chart displays discontinuous data in categories plotted as columns that do not touch.

Did you get all four correct? Well done if you did.

Okay, so we have seen how we can plot continuous data as a histogram.

We can also plot continuous data as a line graph.

However, when you've not got very much data, a line graph doesn't tend to give you very much information because each individual height would be recorded as its own frequency and therefore, we're just going to have frequencies of one going across our graph.

Not terribly useful, especially when there's not very much data.

Really would need thousands of data here in order to be able to make a line graph useful.

But if we did have a lot of data, a line graph can be very helpful and you can see that there.

And if we put a line of best fit through those data points, we can see the trend and the patterns much more easily.

So in this example, for instance, we have the heights in the middle of the range being the most common with far fewer people being much shorter or much taller.

So what do you think? Which graph or graphs would be suitable for plotting continuous data? The line graph, the histogram or the bar chart? I'll give you five seconds to think about it.

Okay, have you decided? Well, hopefully you've chosen the line graph and the histogram.

Well done.

So we're going to plot our data as a histogram because our data is continuous.

So what we need to do is make sure that we've got our data as frequencies, and then when we have our data as frequencies, we can then plot it as a histogram.

So in other words, we're going to have to process our data before we can plot it.

So you're going to need to draw a table of the data ranges, for instance, grouping our heights into 10 centimetre ranges.

Then you're going to go through each individual data point and tally them against the correct range to which they belong.

Once you've got those tallies in place, you can then convert the tallies into numbers of frequency.

So that's the first step that you'll need to do.

And once you have created your table of frequencies, you will then be able to plot a histogram.

So in order to plot a histogram, you'll first of all have to plot the x-axis, which is height.

And in order to do that, you'll need to assign a column for each range, making sure that there are no gaps between any of those columns.

You'll then need to label those columns and also label the axis.

So make sure that the columns are going in the correct order, 130, 140, 150, 160 and so on, for instance.

Once you've done that, you can then plot the y-axis.

So firstly, you'll need to make sure that the y-axis itself goes up in evenly spaced increments.

So my y-axis on this graph goes up in increments of one, one, two, three, four, five, six.

But you might need to use a different range, a different set of numbers.

Then you're going to draw the columns to the correct height, and then you'll need to shade or colour those columns in before you add a label to the axis.

And finally, a label to the title of the graph.

So what do you think? Which label will go on the y-axis? Is it frequency, height, or range? I'll give you five seconds to think about it.

Okay, did you choose frequency? Well done if you did.

So what I'd like you to do is either using your own data that you have collected or if you haven't got any data, use the data that I'm providing on the additional worksheet.

And firstly, you're going to have to convert that data into frequency data using appropriate ranges and a tally.

Once you have converted your data into frequency data, you will then be able to draw a histogram and you will need to make sure that your histogram has labelled axes, an appropriate scale, lines are drawn with a ruler and a pencil, please and a title for the graph.

So pause the video, take your time, and be nice and precise with your drawing and come back to me when you're ready.

Okay, so hopefully, your frequencies will have looked something like this, maybe the height of students or the mass of apples that you measured.

And then your histogram might look a bit like this with your height on the x-axis with frequency on the y or the mass on the x-axis and frequency on the y.

So just check your work over, make sure that you've got your frequencies calculated correctly and your graphs plotted properly as histograms. So well done for having a go at plotting those graphs.

They can be really tricky things to plot.

So I'm sure you've had a really good go.

Well done.

So what we're going to do now is have a look at the data that we've just drawn as a graph.

We're going to analyse it and draw some conclusions from it.

So by looking at the histogram, we can describe the data using the most frequent ranges to start off with and then working out in either direction from there.

So for instance, we can say 11 students in the class were between 150 and 159 centimetres tall, which was the most common range of heights, whereas heights either side of this were less common with only three students being 130 to 139 centimetres tall and only two students being 170 to 179 centimetres, and this being the least common height.

So from the histogram that's on the screen, which summary do you think is most appropriate? Is it A, the range of masses recorded was 19 grammes? Was it B, most apples weighed between 106 grammes and 110 grammes? Or was it C, three apples were the lightest or heaviest? What do you think? I'll give you five seconds to think about it.

Okay.

have you chosen the middle option? Well done if you did.

Most apples weighed between 106 and 110 grammes.

Good job.

So there's a number of factors which influence the characteristics that an organism has.

Some of these are genetic, some of them are environmental and others are lifestyle choices.

Now, continuous variation is usually influenced by many factors, including some genetic and some environment and lifestyle choices.

So if we take height, for instance, height is a continuous variable.

Your maximum height is likely to be dependent in part on your genes, but also with influence by your lifestyle, particularly your diet.

So if you were to live in an area where the diet was poor and food was restricted, your maximum height is likely to be less than it would be had you lived in a place where there was abundant food with a rich diet.

So what do you think to this? The circumference of a tree trunk must only be influenced by the tree's genes.

True or false.

Okay, did you say false for that one? Well done, but can you justify your answer? Okay, have you chosen that features with continuous variation are usually influenced by environmental factors? Well done if you did.

Okay, what I'd like you to do now is have a look at the data that you've just been plotting as a histogram and I'd like you to write a conclusion.

Your conclusion should describe the trends in the data, suggest what type of variation the data shows and a cause for the variation.

Plus also suggest what might not cause the variation.

So pause the video and take your time and come back to me when you're ready.

Okay, so let's see what you might have written.

So your conclusion may be similar to this.

11 students in the class were between 150 and 159 centimetres tall, which was the most common height range.

Heights either side of this were less common with 130 to 139 centimetres featuring only three students, and 170 to 179 centimetres featuring only two students being the least common.

The tallest student was 173 centimetres and the shortest was 136 centimetres, which is a range of 37 centimetres.

And this is an example of continuous variation where the variety in height will be caused by the genetics of the individuals plus their lifestyle, including their diet.

Or if you were concluding data about the mass of apples, maybe you wrote something like this.

Four apples had masses between 106 and 110 grammes, which was the most common.

Only one apple had a mass between 116 and 120 grammes and two between 101 and 105 grammes.

The heaviest apple was 117 grammes and the lightest was 101 grammes, a range of 16 grammes.

This is an example of continuous variation and the variation in mass will be caused by the genetics of the apple tree and its environment, including weather and water availability.

So just have a look over your answers, compare them to mine.

Is there anything you can add to it or have you already gone well beyond what I've written? Well done if you have done.

That's great.

Well done.

So to summarise our lesson today, we've seen that continuous variation of a feature can be measured and plotted as either a histogram or a line graph.

Histograms display continuous data in ranges plotted as columns that touch.

And these are really useful for small datasets because they'll be more suitable than displaying the data as a line graph.

And we've seen how continuous variation has a number of influencing factors, including genetics, environment, and lifestyle.

So I hope you've had a great lesson today.

I certainly have.

Well done for plotting that graph and taking the time to spend a great deal of care over it.

That's really well done indeed.

So thank you for joining me and I hope to see you again soon.

Bye.