Lesson video

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

During today's lesson, we are looking to work with the mode.

We're gonna look to find the mode with data presented as a list, think about what it's actually measuring and how it is measuring.

We've got some keywords for this lesson that we'll be using throughout the whole lesson.

So firstly, the mode.

So the mode is a measure of central tendency and we're gonna discuss a little bit more about what it is, but it's the most common value or class with the largest frequency.

And then some data has no mode or more than one mode.

If data has 2 modes, we say it is bimodal.

And if data has 3 modes, then we would say it is trimodal.

This lesson's got 2 parts.

The first part is about finding a mode.

The second part is it is not always one mode.

So thinking about those words, bimodal, trimodal or potentially no mode.

Let's make a start on the first part.

So which animal appears the most? You've got pictures of elephants and pictures of giraffes.

Which one appears the most? A little count.

We can see that the elephant is there more than the giraffe.

Lucas empties his wallet.

Which coin does he have most of? 5p coin.

So there is more 5ps than there are any other coin on that screen.

Which letter appears the most on the keywords slides? So here is a exact copy of the keyword slide that we've already seen.

Which letter appears the most on that slide? And the letter is e, it appears 28 times.

If you wish to check that, then pause the video and you can do some counting.

You probably had an idea that it was gonna be a vowel, but e appears 28 at times, so it's the most common one on that slide.

So elephant, the images of the elephant, the 5p coin and e were the modes of the data and they were quite easy to identify.

It was all about just looking for the thing that appears more than the other thing.

So when there was the elephant and the giraffe, counting them up, how many elephants pictures were there, how many giraffes were there? And comparing them for the 5, the coins, I think it was quite obvious straight away that the 5p was there more often than the other ones in Lucas's wallet.

With the text, that took a longer time to actually check which letter appears the most, but it's just identifying which one comes up more than the others.

So a quick check, what is the modal fruit? So here you've got some images, icons of lemons, pears, apples and oranges.

Which one is the modal fruit? Pause the video whilst you make your decision and then come back and we'll check that you've got that right.

Hopefully you've got the lemon.

So here I've just reorganised it a little bit like a bar chart or pictogram really, infographic that we've got them in their sort of their categories, it's much easier therefore to see that the lemon is there more times than the pear, the orange and the apple.

So data is gonna be collected about months of birth.

Aisha has a January birthday, Sam has a May birthday, Jacob, December.

So which month is the most common? So at the moment there's 3 pupils.

None of them have got the same birth month as each other.

So there's not a repeated month.

If we continue to find out about more pupil's birthdays, we've got Lucas in September, Laura in April, and Alex in July.

So which month is the most common now? So there is still no repeated month.

The sample is relatively small and so to not have repeats is fairly likely.

And so we would say that the data has no mode.

There is nothing that appears more often than any of the others.

They've all appeared one time in this sample of 6.

But bearing in mind that the sample here is small, we've not asked a lot of people and so we are not, it's not uncommon that you're gonna find that this idea that there is no mode.

So the mode is another average.

You may have previously learned about the mean as an average and the median as an average.

The mode is another average.

It's another measure of central tendency and we use it to analyse data.

Smaller data sets, as we just saw, may not have a mode and so the mode may not be a very useful measure of central tendency for smaller data sets.

However, the mode is very useful as one of the averages because you can find the mode for qualitative data like we saw with the animals or the coins and colours, et cetera.

The mode has got issues when it comes to smaller data sets that you might just not have a mode.

The data may have no mode because there just isn't enough data really to see a mode.

But sometimes you will with a small data set.

But what is useful about the mode is you can 'cause it's just about how many, what comes up more than another that when you've got data that is non-numerical, then you can find a mode.

Here we've got data about shoe size in a class and represented as a dot plot and we can see that the most common shoe size is size 7.

It's the size with the most dots.

Izzy has said, "but size 6 and size 9 both have 5 dots, so 5 is the most common." And so what Izzy has commented on is the most common frequency but not the most common shoe size.

So it's really important that when we're analysing our data and we're trying to find any average, but especially the mode, you are looking for the mode in the context of the data.

So this data was about shoe size and so the most common shoe size is the one with the most frequency.

And this can happen, it is quite common for people to get confused about.

And it's important that you are always remembering that it's the one that appears or occurs the most.

So it doesn't matter if there are many bars of 5, the shoe size 7 had the most pieces of data that were a 7.

If this was a list of data, our list would be 4, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8.

Because I've said the 7 more than all the others, the 7 is the most common.

There are more 7s in my data than any other number.

So it's really being careful that you are looking for the highest frequency, the most common and the one that appears the most.

Here's a check for you.

So in a year 8 class data is collected about shoe size, what is the modal shoe size in this year 8 class? Pause the video whilst you have a go at that and then press play to check your answer.

So the modal shoe size is 6.

If you look that's the one with the most dots.

So the most things of that size.

So we're now onto the practise part for finding the mode.

So on this screen we've got 3 questions for you to have a go at.

So whilst you're trying those, pause the video and then when you're ready for the next question, press play.

So question 4, Sofia was rolling an 8 sided dice, "I rolled a 6 ten times, I rolled a 7 twelve times, I rolled an 8 ten times." What was the mode score on a roll of the dice? I would suggest you read that again, think about what the data is about and then answer, pause the video whilst you're doing all of that, and then when you are ready we're gonna go through the answers to all the questions.

So question 1, what was the modal animal? It was the spider so the spider was there 4 times compared to there being 3 beetles, 3 cats and 2 dogs.

So it was a case of comparing how many of each of the animals, counting them up and then which one had the most.

Question 2, in this set of data, what is the mode? And 1 is the mode.

It appears 6 times, which is the most compared to any of the other data values.

Question 3, in this set of data, what is the mode? And the mode is 18.

You didn't need to order it but question 2 was already ordered and therefore they were in their groups of numbers.

So counting them up was very easy.

When the data is unordered, then you might be, there's an opportunity for you to miss one of them in your counting.

So by ordering it first, it's all groups them up for any repeats and then you can see which one has occurred more than the others more clearly.

So I would encourage you to order data if you've got a list of data, even if you're trying to find the mode.

So question 4, 7 is the mode roll.

So this one was tricky with the wording.

The question was what was the mode roll? So she rolled a 6, she rolled a 7 and she rolled an 8.

So they are one of those numbers is the answer, in the case it's 7, and the reason it's 7 is because she rolled 7 more times than any of the others.

So just being really careful and thinking about what the data is actually about.

So this data was about what number appeared on the 8 sided dice.

We're now up to the second part of the lesson and so is it, it is not always one mode.

So thinking about data where there's not only one mode.

In the first learning cycle, we've seen that small data sets may not have a mode, larger data sets are more likely to have a mode.

So on this dot plot, the dots are fairly small, but on this dot plot, there are 52 points and there is only one mode.

So even though 52 is a relatively large amount of data points compared to what we've been working with previously, there still only came out as one repeat.

There is a chance that still no repeats happened.

We know that smaller data sets may not have a mode just by chance.

Larger data sets are more likely to have a repeated number.

So this dot plot shows the European shoe sizes of groups of pupils.

7 is the highest frequency and the modal shoe size is 31.

5 and 40.

So we would say this data is bimodal, it's got 2 shoe sizes of the same frequency.

And so that's our modes.

The shoe sizes, the data is about the shoe size but because there are 2 of them we say it's bimodal.

So bi as a prefix meaning 2.

So bicycle, a bike with 2 wheels as opposed to a tricycle, which is a bike with 3 wheels.

Bisect, another word that you would use in mathematics to cut into 2 equal parts.

So the bi is a prefix for 2.

So this data is bimodal, it's got 2 modes, one at 31.

5 and one at 40.

If you remember earlier in the lesson back when Izzy thought the mode was different to the actual answer and her reason for that was because the frequency, there were 2 shoe sizes, in the earlier example with Izzy, there were 2 shoe sizes that appeared the same amount of times as each other.

And here we need to be careful as well.

So this data is bimodal with 31.

5 and 40 because 7 is the highest frequency.

Some people may be thinking, but what about the shoe size 30 and 30.

5 and 39 and 41 because there are all 4 of those appear 6 times and 4 is more than 2.

But the issue we've got or the thing we need to be careful of is that you are always looking for the highest frequency first.

So 7 is the highest frequency.

Yes, there are more shoe sizes where they have 6 of each, but 6 is not bigger than 7.

So 7 is the most common.

So we need to make sure we are always identifying the highest frequency, the tallest in the dot plot, the one that goes up the highest 'cause it's got the most dots.

That's where the mode will appear.

If you've then got a repeat of that tallest one, that's when we've now got bimodal data.

Looking at the dot plot though, we can kind of see that there seems to be 2 subgroups.

Subgroup A and subgroup B.

Why might this be? So subgroup A may be a younger class and subgroup B might be an older class because all it says is it's a European shoe sizes of a group of pupils and within one school, you are gonna have an array of different shoe sizes because of the younger years up to the older years.

If we ask more pupils about their shoe size, we've got this dot plot.

And so now the data has become trimodal and this extra pupils have put some more data on and our data has now got 3 highest points.

All of them have still got a frequency of 7, but we've got this, we've got an extra data.

So the modal shoe sizes are now 31.

5 that was previously lit there, 35, so the new data has increased, has put that mode on and the 40 from previous.

So trimodal data sets where there are 3 values that occur the same amount of times as each other but the highest amount.

So a check, data can only have one mode, true or false.

So that's false.

We just saw that we've had data with more than one mode.

Now justify your answer.

The data might not have any mode.

The data might have no mode, one mode, two or more modes.

So that's b.

So it's true that the data might not have any mode, but that's not the only scenario.

It could have no mode.

It might have one mode but it could have 2 or more modes.

So now we're onto the practise part of the second cycle.

And the first 3 questions are similar in what you need to do, but you do need to think about them.

So question one, write a data set of 20 that is bimodal.

Question 2, write a data set of 10 that has no mode.

Question 3, write a data set of 20 that is trimodal.

So pause the video whilst you're coming up with them.

You could always find more than one set for each question if you wanted to think about what your data might actually be collected about as well.

So pause the video whilst you're doing that and then when you're ready, we'll move on to the next question.

So on this question 4, there are 4 dot plots on the screen and what I want you to do for each one is write down how many modes the data has, if any.

So it's not about the value of the mode 'cause I know it's very small, but instead by looking at the distribution of the data, how many modes does it have? Pause the video whilst you are getting on with that question.

And then when you come back, there's one more question to do before we'll go through the answers.

Question 5, what is the mode of the data shown on this dot plot? So this one is about given the actual value of the mode rather than just how many pieces, how many modes there are, if there are any.

So pause the video whilst you are doing that.

And then when you come back, we're gonna go through the answers to these 5 questions.

Question one needed you to come up with your own data set of 20 pieces of data and it had to be bimodal.

So there is a chance that we've got exactly the same one, but it's highly unlikely.

So you just need to check that what mine, the key parts of mine are on the same as yours.

As I said, when you were getting started, you could try and do more than one for each of these.

So there are multiple correct answers and you should have 2 values that are repeated the same number of times as each other.

So my example here, there are 20 pieces of data.

If you were to count how many there were, there's 20 and the 0 appears 3 times the 1 appears 2 times, the 2 appears 2 times, the 3 appears 3 times, the 4 appears 4 times, the 5 appears 4 times, the 6 appears 2 times.

So the highest amount of each number is 4 and there are 4 4s and 4 5s.

So that's why it's bimodal because no other number appears more than 4 times.

So 4 is our highest frequency, but because there are 4 4s and 4 5s, then this is bimodal data.

So my modes here would be 4 and 5.

So once again yours is not gonna be necessarily the same data set as mine, but you should have 20 pieces of data.

They could be positive, they could be negative, they could be decimal or just integers like mine.

But the key thing is that 2 of the numbers, 2 of the values appear the same amount of times as each other and more than any others.

Then question 2, question 2, write a data set of 10 that has no mode.

This is probably the easiest out of all of them.

You just needed to make sure that nothing appeared more than anything else and there were 10 of them.

So here, multiple correct answer this, nothing should occur more than anything else.

I went for, because the mode can be qualitative data, I went for colours, so pink, white, red, blue, green, orange, brown, yellow, purple until none of them appear.

None of them have been repeated.

So there is no mode, none of them appear any more times than another.

If, if I had put 2 oranges in that list, then the orange would've been the mode because it would've appeared twice and everything else only appeared once.

So your answer, the important thing is that nothing appears more times than anything else.

Question 3, you needed another data set of 20 and this time it had to be trimodal.

It may have been that you just altered your answer to question one 'cause you had 20 pieces of data slightly to make it trimodal or you may have done a completely different data set.

I went for just an alteration, a slight adjustment to question one.

And what I've done is I have got, now I've got 4 3s, 4 4s, and 4 5s.

So the highest frequency is still 4, but this time there are 4 3s, 4 4s, and 4 5s.

So there are 3 values that appear 4 times and that's what makes it trimodal.

So making sure that you have the highest frequency appears on 3 different values.

You needed to say, how many modes, if there were any.

So the first one is bimodal.

It's bimodal because those tallest, if you look at them sort of like bars if you like of dots.

The tallest bars, there are 2 of the same height, which are the tallest.

So it's bimodal, that's the top left.

The top right is trimodal because the tallest amount of dots happens 3 times.

The bottom left is also trimodal.

So again, you've got 3 stacks of dots of the same height and they are the tallest.

And then the bottom right there is only one mode.

So the tallest bar only, there's only one of them at that height.

So it's the highest one identifies the mode, but if you've got copies or multiples of the highest one, that's when you start to have bimodal or trimodal data.

Question 5, what is the mode of the data shown on the dot plot? So the data is actually bimodal.

We've got 2 tallest ones of the same height and they are 74.

5 and 80.

So again, when you look at the data here, the distribution, it kind of does look like there's 2 subgroups within this data collection as well.

So that's why there's sort of 2 modes To summarise today, which this lesson, which is about understanding the mode.

So the mode is a measure of central tendency.

It's the most frequently occurring value or object in a dataset.

And it can be used for non-numerical data.

So we saw that with colours and months, et cetera.

So there can be, data can have no mode, but it can have more than one mode as well.

So data that does have more than one mode can be classified as bimodal if there are 2 modes or trimodal if there are 3 modes.

Hopefully you've enjoyed today's lesson.

I look forward to working with you again in the future.