Lesson video

Hello, I'm Mrs. Lashley and I'm really looking forward to working with you throughout this lesson.

In our lesson today, we're gonna be working with calculating the mode from different representations.

So from frequency tables and from different types of graphs.

On the screen at the moment you can see words that hopefully you're familiar with from previous learning, things that you've already done.

But I would encourage you to pause the video and reread them just to re-familiarize yourself as we will be using them in the lesson today.

So our lesson has got three parts to it.

The first part, we're gonna be looking at the mode from a frequency table.

The second part we're gonna look at modes from a bar chart.

And then the last learning cycle will be looking at modes from line graphs.

We are gonna make a start now with the frequency tables.

On the screen we've got a relatively small list of data and it's quite clear, because it is ordered, it is quite clear that we can see that 14 would be the mode.

It occurs more often than any other number in that list.

That same data can be represented as a frequency table.

So there are two 12s, there is one 13, et cetera.

The mode can become less clear and we're gonna talk about why.

This frequency table has got some data that's showing the number of reviews for each rating at a hotel.

So you can rate it from one, rate it up to a five and we can see how many of each of those they have got from the frequency table.

So Lucas said, "There are two 12s, so the mode is 12." And you can see where Lucas has said that there are two 12s in that frequency column.

12 occurs more often than any of the others.

So the mode is 12 is what Lucas is saying.

Jacob says, "There are two 12s, so the modes are 1 and 2." Alex says, "The rating with the highest frequency is 5." And Andeep has said, "The highest number is 28 that is the mode." So are any of these pupils correct about this data? Alex is correct.

So the data is about ratings.

We always need to remember the context that the data is in.

And this data is about ratings for a hotel.

So the mode needs to be one of the ratings.

So Lucas said, "There are two 12s.

So the mode is 12." Well, nobody gave the hotel a rating of 12, so the mode cannot be 12.

Jacob said, "There are two 12s, so the modes are 1 and 2." So Jacob did give the mode in the context of the data, but there are two 12s, but the mode is the one that appears the most.

So Andeep identified that the highest number, the highest frequency was 28, but that's not context again.

So that's an indicator of where the mode is, but isn't the mode.

So it was Alex that has said, "The rating with the highest frequency is 5." So we need to be careful with the frequency table that it's not about looking for the frequency that appears the most, it's looking for the frequency that is the highest that indicates that that one has appeared the most and then giving it in its context.

So you thinking about all of that, here is a check, which frequency table shows data with a mode of one? Pause the video whilst you are looking through those frequency tables and being very careful.

And then when you think you know what the answer is, press play so that we can check.

I'm hoping that you went for B.

If we go through why the other two were not correct.

So on the frequency table at A, the highest frequency was 52, which means that the rating, the mode would be 3.

On C, the highest frequency was 19 and that was on a rating of 5.

So the mode would be 5.

Whereas B, which was correct, the highest frequency was 120 and that was for the rating of 1.

So the mode was 1.

This frequency table is about pet collars and their colour.

So you may remember from learning previously that mode is an average that can be used on qualitative data.

So here we've got data about colours and so we can think about the mode on this.

The highest frequency is 21, it appears twice.

So in that frequency column there are two 21s, 21 is the highest number and there are two of them.

So this data is said to be bimodal.

Remember that we need to give it in the context.

And so it's colours of pet collars, the modal colours are blue and yellow.

The frequency is what indicates the mode, but that isn't the mode.

So being very careful to always give it back in the context.

So now you're gonna do a bit of practise working with mode from a frequency table.

You've got two questions, but the first one's here.

So if you have a go at the first one, you need to work out the mode for each frequency.

But if there isn't a mode then you can write no mode.

Pause the video whilst you're doing it and then when you come back we'll go on to question two.

So here we've got a data set of 50 and you need to fill in the missing frequency and write down the mode number of goals scored.

So working with the frequency table, you know that it's representing 50 pieces of data.

You need to complete the frequency table and write down the mode number of goals scored.

Pause the video whilst you work that answer out.

And then when you are ready to come back we will go through the answers to question one and question two.

Question one, what's the mode? And if there isn't one, just write no mode.

So the first table was about animals, the highest frequency was 24.

So the mode would be cat.

The second one was about goals.

The highest frequency is 24 and there is two of them.

So the goals one and two, it was bimodal.

The last one, the highest is 12, but they all are 12.

So we would say that there is no mode, nothing appears more often than any others, okay? So once you start to have all of them the same, it's not useful to say that it's got many modes.

So we'd say it's got no modes.

Question two, we needed to use the idea that there is 50 pieces of data in total to calculate the missing frequency.

And then from that you could decide which one was the highest frequency.

So the missing frequency was nine because if you added up the ones you had and subtracted from 50, you were left with nine, which means that three goals scored is the mode because 21 is the highest frequency.

I'm hoping that you didn't fall into the trap of there are two nines and therefore it's bimodal.

No, because nine is not the highest number, 21 is the highest number.

So if there had been two 21s then it would've been bimodal.

But there is only one 21, 21 is the highest.

So the mode is three goals scored.

We are now gonna move on to the second part of the lesson.

And that is finding the mode or calculating the mode from bar charts.

So scores for a game have been collected and are shown in the frequency table.

This frequency table shows that the mode is zero because it has the greatest frequency.

If you look down that frequency column 45 is greater than any of the other numbers.

It doesn't matter that 31 appears twice because 31 is less than 45.

So 45 is the greatest number there and hence the mode is zero.

So like a frequency table where you identify the greatest frequency, in a bar chart, you're gonna identify the tallest bar or bars if it was bimodal.

So this bar is the tallest, the mode is zero.

There are two bars of the same height, but they're not the tallest.

So there is not bimodal.

So again, really thinking about you need to find the tallest first.

If there were two of the same heights, which were the tallest, then it would be bimodal.

It doesn't matter, all the bars that are shorter than the tallest one, do not matter.

They will not influence the mode.

So the mode is about the one that appears the most and we are gonna find that using the frequency.

So these are frequency bar charts, thinking about how many pieces of data are represented on each of the bars.

So just to check, on a bar chart, the mode is the most frequent height, the frequency of the tallest bar, or the context of the tallest bar? Pause the video whilst you are considering what you think the right answer is and then when you're ready to check that press play and come back.

You may have gone for B.

And although the frequency of the tallest bar is important, it's not the mode.

So the mode is the context of the tallest bar.

So the frequency is the one that indicates which one it is, but it's not the mode.

So again, always being careful and mindful that when you are doing your analysis and using a measure of central tendency, it's about the context of the data.

So the mode will be about the context.

On the screen you've got a bar chart that Lucas has created following a collection of data about flags that his friends can recognise.

And the data is bimodal.

Lucas says, "How do we know it is bimodal?" And Aisha says, "It's bimodal because there are two pairs of equal bars." And Sam says, "It is bimodal, because there are two of the tallest bar." So who is correct? So Aisha is talking about the fact that France and UK have the same height and Spain and Sweden have the same height.

So she's saying we've got two pairs of equal bars and bimodal means two modes.

So that's why Aisha thinks this is bimodal.

Whereas Sam is saying that it's bimodal because there are two of the tallest bar.

So the tall bar is 14 and we've got two fourteens, one for France and one for UK.

And that's why Sam is saying the data is bimodal.

And so Sam is correct because the mode is all about the one that occurs the most.

If there is data that appears the same amount and it is the most still, then it becomes bimodal.

So because France was recognised 14 times and UK was recognised 14 times and that was more times than any other flag, they are both modes and the data is bimodal.

So a check on that, which of these bar charts shows data that is trimodal? So pause the video whilst you're making your decisions and then come back to check it.

I'm hoping that you went for bar chart C and that's because the tallest bar is seven and three bars occur with a frequency of seven.

On A, there are three bars of equal heights, but they're the shortest bars so they're not the mode.

On B, we've got three pairs of equal bars, but the highest bar is seven and there is only two of them.

So the data shown in A has one mode.

The data shown in B is bimodal, it's got two modes.

And the data shown in C is trimodal.

It's got three modes.

So really making sure you're always trying to find that tallest bar first and then look to see if there are any other bars of the same height.

Laura's got some homework and it's to complete a bar chart.

The task tells her that the data is trimodal.

So remembering that trimodal means there are three modes.

There are 600 pieces of data.

The bars one, three and five are missing from the bar chart.

So they're the ones that she needs to add to complete the bar chart.

Laura remembers that Trimodal means that there will be three of the tallest bars.

But which is the tallest.

So the zero bar has the greatest frequency of 90, so three bars of heights 90.

So Laura's added bar one and bar three and made them both have a height of 90.

So now that the data is trimodal, there needs to be a total frequency of 600.

We were told in the task that 600 pieces of data are being represented on the bar chart.

So currently there is a total of 420.

We can work that out by adding up the frequencies for each bar, which means that the score five would have to have a frequency of 180 in order to have a total 600.

And now adding that bar of 180, the data is no longer trimodal.

So we started by looking at the tallest bar, which was 90, made sure there were three of the nineties so that it was trimodal, and then looked at what was remaining and put that as our final bar.

That final bar was over 90 and therefore the data has gone from in Trimodal to just having one mode.

And therefore this task isn't completed.

It hasn't worked, our data is no longer trimodal.

So we're gonna have to start again and think about this in a different way.

So we're going back to the original bar chart that was given in Laura's homework.

We've got the missing bars at one, three, and five.

So Laura decides she's gonna try this a different way by starting with the total.

So last time we dealt with the trimodal and then did the 600 and we didn't get to the correct answer.

So she's decided we'll try again, but we're gonna try it in the opposite way.

So we're gonna think about the 600 first.

So currently the given bar chart represents 240, which means there is a remainder of 360 pieces of data to be added onto the bar chart.

The data is also trimodal.

So the three bars need to be equal heights and taller than the other three in order to be Trimodal 360 is how many data points we've got left and we need them to go across three bars and we need them to be equal.

So that's why division as an operation is good.

It shares evenly and that means 120.

So she's now completed her homework.

She's got 600 pieces of data represented on the bar chart across all six bars.

It's trimodal because there are three bars of equal heights of which they are the tallest compared to all the other three.

Izzy has the same homework and submits this.

Why is it incorrect? So this is for you to have a think about.

So pause the video whilst you're thinking, why is this incorrect? What has Izzy done wrong? And then when you're ready to check that, press play and we'll move on.

Izzy is wrong because it doesn't have a total frequency of 600.

So if you were to add all of those bars up, it doesn't equal 600.

It has three pairs of equal bars, but that isn't the definition of trimodal.

So her bar chart represents bimodal data because the tallest bars, there are two of them.

So there are two tallest bars and that makes it bimodal, not trimodal.

You're gonna do some practise on modes from bar charts.

So question one, what is the mode on each of these bar charts? Pause the video whilst you are answering that question and then press play to come back for question two.

Question two, the data is bimodal.

Complete the bar chart.

Pause the video whilst you're thinking about that.

When you've got an answer, check it, is it bimodal? Have you kept it bimodal? When you're ready for question three, come back.

So on question three you are told there are 100 of data to be represented on a bar chart.

The data is bimodal and you need to add the two missing bars to the bar chart.

Pause the video whilst you are working that one out.

And then when you're ready to go through the answers to questions one, two, and three, press play.

And we'll make a start.

Question one, it was identifying the mode on each of the bar charts.

So these are frequency bar charts, you're looking for the tallest bar and so on question part A carriage 1 had the most occupied seats and part B size four was the most common shoe size.

Question two, the data was bimodal and you needed to complete the bar chart.

So bimodal means it has two that appear the most, more than any others.

So you were originally given cat with a frequency of 18 and so you needed to add the hamster.

So they also had a frequency of 18.

That way we had two bars of the same height that were taller than any others and that's what makes it bimodal.

Question three, you needed to add the bar for oak and pine.

So a hundred pieces of data are represented on a bar chart.

The data is bimodal.

Add the two missing bars.

So this is very similar to Laura's homework.

So firstly you needed to work out how many pieces of data was left to be represented.

So adding up ash, beach, sycamore, robin, maple and birch.

And you would've worked out that there were 60 pieces of data on the bar chart already.

So that meant there was 40 left to be represented with over two bars, which would mean 20 on each and that makes it bimodal 'cause 20 is higher than any other frequency.

And if both of them are 20, then that makes it the bimodal part.

So we're now up to the last part, the final part of today's lesson, and that is mode from the line graphs.

The picture here shows the five tallest buildings in the world.

What's the most common height? Do you agree with Izzy that the tallest is about 825 metres? Do you agree with Sophia and say that C and D are the same height? So 600 metres.

So the data that is shown in that picture is approximately 825 metres, 625 metres, 600 metres, another 600 metres, and 550 metres.

So the mode would be 600 metres because it appears more than any other value.

So Sophia was correct rather than Izzy.

So with the bar charts we were looking for the tallest, but this isn't a bar chart.

This was a picture that shows the heights of five tallest buildings.

And the question was what was the most common height? So you wanted the one that appeared the most, not the tallest, but the height that appeared the most.

And there were two buildings of 600 metres approximately.

So 600 metres would be the one that appeared more times.

We can see here on the left you've got a bar chart showing shoe sizes in a group of pupils and it's a frequency bar chart.

So each of those bars represents a different amount of pupils.

And on the right hand side we've got a line graph that shows weekly hits on a website.

So in week one and the unit is thousands.

So in week one there was 1000 hits on the website and week two there were 2000 hits.

So the difference between the bar chart and the line graph is that the bars represent multiple pieces of data, whereas the line graph is a single value at each point.

And this is where we are working with frequency bar charts.

You could do the data for the weekly hits on a website as a bar chart and the height would just be the hits.

We've previously looked at bar charts, frequency bar charts, and finding the mode from those.

And that's where you look for the tallest.

Because they represent data in different ways, so the bar chart on the left, the frequency bar chart is representing multiple pieces of data on each bar, whereas the line graph is representing one piece of data at each point.

We find the mode differently.

So on the bar chart it's the tallest bar because it's got the most amount of data points there.

So size four would be the mode on the bar chart.

On the line graph we are looking for, it's more similar to that building's one that we are looking for the most points at the same horizontal value.

And so for the data here about that website, it would be 1000 hits because there were three data points on the thousand line compared to any others other horizontal lines.

So a quick check for you.

So the mode on a line graph is the highest point, true or false? And then justify your answer.

Pause the video whilst you are considering that and then when you're ready to check it, just come back and press play.

So that's false.

And the justification is the mode is the data value that appears the most.

So we've got a line graph here that represents the average daily minimum temperature in 2022 in Aberporth.

So what is the modal temperature in Aberporth in 2022? So by using a straight edge and a ruler is one that you've probably got to hand, you can move up the graph, counting the points on each horizontal line.

So here's my ruler that, it's not about it being a ruler, it's not about being able to measure, it's about being a straight edge and keeping us horizontal.

So the first data point that I meet as I move up the vertical scale is 2 degrees and the ruler is only hitting one point.

So 2 degrees occurs one time.

If I move it up, I hit a point at 4 degrees.

And again, if I look across my horizontal line, my ruler, there is only one data point on that line.

So 4 degrees Celsius occurs one time.

Moving the ruler up again, now I hit two data points, 5 degrees occurs twice.

So you can see there that the ruler on that level is at 5 degrees Celsius in terms of temperature.

And there are two data points on that same horizontal level.

So currently the mode would be five because it's occurred more times than any of the other temperatures.

Moving up, 6 degrees occurs only one time.

So the mode would still be 5.

8 degrees occurs one time, 10 degrees occurs one time, 11 degrees occurs two times.

So now we've had 5 degrees occurring two times and 11 degrees occurring two times.

So now the data has become bimodal because two is the highest frequency, that's more often than any others, but it's happened twice.

So it's bimodal.

12 degrees only occurs one time, 13 one time, and 14 one time.

So 5 degrees and 11 degrees both occurred two times.

They're both the modal temperatures and therefore the data is bimodal.

So it wasn't the highest temperature, that wasn't what the mode was.

The mode was the temperature that appears the most and we use this horizontal.

So using a ruler, using a straight edge to work up the graph and looking at how many times the data points appear on each of those levels.

So a check for you, what is the modal temperature in the classroom? So we've got data about temperature in a classroom from 9:00 AM till 3:00 PM and what would be the modal temperature? Pause the video whilst you work that one out and then press play to come back.

So the modal temperature is 18 degrees Celsius.

If you used a ruler or a straight edge, 15 degrees only happened once, 17 degrees happened once, 18 degrees happened three times at 10:00 AM, 11:00 AM, and at 2:00 PM then it went up to 20 degrees and then 21 degrees.

But that only happened once each.

So three was the highest frequency and therefore our modal temperature, making sure we're giving it in the context of the data, is 18 degrees Celsius.

So we're up to the practise part of this section of the lesson, there's only the one question, but you've got to do the sort of three questions in the one.

So what is the modal temperature for each of the places represented on this line graph? The data is about the daily temperature rounded to the nearest degree Celsius in 2022 for those three different places in the UK.

Pause the video whilst you're working out the mode for each place and then press play to come back and check your answers.

Bradford, which was the blue with the square points, there had no mode, there was no temperature that appeared more than once.

And so because they all appeared once we would say there was no mode.

Eastbourne was trimodal.

So 14 degrees, 18 degrees, and 24 degrees all appeared twice over the course of the year.

So it was trimodal.

None appeared more than twice.

So there wasn't anything that beat them, which is why all three of them are our modes, trimodal.

And Tiree is bimodal, 9 degrees and 16 degrees both appeared twice.

So they both appeared twice, twice was more than any of the others.

There was nothing that appeared more than twice.

And so that's why it's the highest frequency.

And so it is a bimodal set of data.

So to summarise the lesson, which was calculating the mode from frequency tables and different graphs, the mode can be found on a frequency table by looking for the greatest frequency.

The mode can be found on a bar chart by identifying the tallest bar and the mode can be found on a line graph by identifying the horizontal with the most data points.

Well done today, and I look forward to working with you again in the future.