Lesson video

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

So, during this lesson we're gonna be working with the range, working out what it is measuring, how it's measuring it, and calculating the range from various different representations of data.

So, data is a word that we'll be using a lot during the lesson.

It's a word that you've met before, and data are a collection of information.

Keywords that we are introducing this lesson are on the screen now, and it's the range which the lesson is all about and spread and dispersion.

We will be working with both of these words in the lesson so the definitions hopefully will become more clear as we go through.

So, the range is a measure of spread and it is found by finding the difference between the two extreme points; the lowest and highest values.

And spread and dispersion of data is how varied they are.

So as I say, we're gonna be working with them during the lesson and looking at how we measure it, what it's actually measuring, why we use it from different points.

The lesson has got two parts.

So, firstly just what is the range? So identify what it is, why we use it, how we use it? And then, the second part of the lesson is looking at extreme values in different representations.

So, when data is represented in various ways.

So, we're gonna make a start on that first learning cycle where we're really gonna get to grips with what is the range.

So, on the screen there are two dot plots.

Which dot plot shows more spread out data? Well, B shows more spread out data and the arrows there should hopefully identify why that is more spread out.

Now, we've got lists of data, so which data is more spread out? The list A or the list B? A is more spread out.

So, thinking about that word spread about how varied the numbers are.

The A is varied.

It goes from 5 up to 960, whereas B starts at 15 and goes to 96.

So it's still fairly spread, that dataset B, but not as spread as A.

On a school trip, Izzy and Aisha get to try archery.

You can see on the screen the scores that Izzy got with her arrows, and also the scores that Aisha got with her arrows.

So, archery is a sport where you've got a bow and an arrow and you are firing it at the target.

So, they are the scores that they both got.

Who was more consistent when they tried archery? So, we would say that Aisha was more consistent because her data was less spread out.

Her scores were less varied.

And so therefore, she was more consistent.

Whereas Izzy had zero so she missed the board, the target up to a 10 once she got the centre part of the target.

The range is a measure of how spread out or dispersed data is and it's calculated using the two extreme values in the dataset, the lowest and the highest.

And on a dot plot, the range here is represented by the arrow.

So, on that very first slide where it's held which data set was more spread out and it was dot plots, the one with the longest arrow, the arrow that was going between the lowest and the highest value.

As long as the scale's the same, then you can compare the length of that arrow.

The length is the difference between the two extreme points.

And so for this one, the range would be 17.

The range tells us how dispersed or spread out the data is.

And so, this one has a range of 17.

So, from the smallest up to the biggest, there is a difference of 17.

So, I'm gonna go through one, and then there's one for you to have a go at.

So, here we've got another dot plot.

So, what is the range of this data? So, you need to identify the extreme values.

So, 19 is the lowest and 30 is the highest.

And then, you need to work out the difference.

So, the range is a single value and you need to work it out using the two extreme values.

So it's that difference between.

So in this case, it's 11.

30 minus 19 is 11.

So here is a dot plot for you to work out the range from.

So, pause the video whilst you are working out the range, then press play when you want to check your answers.

Hopefully you identified your extreme values first.

So, 23 is your lowest and 32 is your highest.

So the range is the difference between them.

So, 32 minus 23 is 9.

You need to have the 9.

The range is 9.

So, here we've got a golf scorecard.

There's 18 holes on a normal golf course and they have written down their score above or below par.

So, they've not written down how many shots they took per hole, but instead they've written down whether that was above or below the par score.

So, on hole one they've written -1 and that's because they shot 1 under the par score.

If they were expected to take four shots on hole one, this golfer did it in three.

They were 1 under par.

So, we can see how they did across the 18 holes.

The golfer scores from 2 under par, so that was on hole 11, to 2 over par which was on the 18th hole.

So we can say that their range, they have a range of 4.

There is a difference between 2 and -2.

That difference is 4.

So, even if data includes negative numbers, we still will talk about the range as the difference.

So, that gap between that negative all the way up to the most positive number.

If we think about data of air temperature on an autumn day and we are told that the range of the temperature is 9 degrees Celsius, what does that tell us? Well, that tells us that the data has a difference.

The two extreme values of the data has a difference of 9 degrees.

So that whatever the lowest temperature is, if you add nine to it, you get to the highest temperature.

Or whatever the highest temperature is, if you subtract nine, you get to the lowest temperature.

So there is a difference, there is a gap of 9 degrees.

If we are then told that the hottest temperature recorded was 16 degrees, we can use that to work out what the coldest temperature recorded was because of the range being this difference or how spread out the data is between the two extreme values.

So on a number line, if you think of it like a thermometer, if hottest is 16 degrees Celsius and there needs to be this gap of 9 degrees between the coldest and the hottest, then we can use subtraction to get from our hottest to our coldest.

And that would be 7 degrees Celsius.

Because you're asking yourself, "What is 9 degrees lower than 7?" What is 9 degrees lower than 16 degrees Celsius? So, that range of data.

So just to check, similar to the one we've just gone through.

Over the course of a month, the temperature is recorded at midday.

The lowest recorded temperature is -4 degrees Celsius and the range is 22 degrees Celsius.

What was the highest recorded temperature that month? Pause the video whilst you work the answer out and then press play to continue.

So, 18 degrees.

If you knew that the lowest was -4 and the range was 22, this time you're gonna add 22 onto the lowest 'cause the higher value is 22 degrees away from -4.

So, 18 degrees.

You are now gonna do some practise for the first part of this lesson.

The first part of the lesson was all about what is the range.

Hopefully you've got the idea that the range is the difference between the two extreme values in the dataset.

So for question one, they are dot plots and you need to work out the range for each of them.

Pause the video whilst you're doing that and then when you come back you've got further questions to try.

Welcome back.

So, question 2, you need to work out the range for each of the three data sets that are given there.

So pause the video, work out the range, make sure you are working it out.

It's not just leaving it as a calculation.

What is the difference? And then when you come back there's another question for you to have a try.

Okay, so question 3.

Laura had just finished her homework on working out the range when her ink pen started to leak.

What values has the ink spoiled? So, for each question there is a missing value because the ink has now gone on top of it.

So, pause the video and work out the answer for each question.

We're gonna go through the answers to those three questions now.

So question one, there was two dot plots.

You needed to calculate the range for each of them.

So, you needed to first of all identify the extreme values and then find the difference between them.

On a dot plot, we can think about the arrow representing that spread.

How spread out the data is.

So, 34 minus 20 is 14.

The range of the data on A is 14.

On B, the data ranges between 72 and 58.

So, the difference is 14.

And so, our range is 14.

Question 2 was where you needed to work out the range, which is now presented as a list of data rather than a dot plot.

You still need to do the same thing, which is to identify the extreme values and find the difference between them.

So on part A, the two extremes are 20 and -1.

The difference between them is 21.

So the range was 21.

Part B.

The data was not ordered.

So you need to be, you don't have to order it to calculate the range, but you do need to, when you're scanning through, you need to be very careful that you don't miss anything.

So ordering it allows you to find the extremes very easy because by being ordered, you go from the smallest to the largest.

And you need the smallest and you need the largest for the range.

So you don't have to order it, but it can be useful.

So the largest in this dataset was a 6 and the lowest was -9.

The difference was 15.

So, that data varies from -9 up to 6, so 15.

And for part C, we've got some decimals in our data set, which is fairly common depending on what you're measuring.

Again, it's not ordered.

If you put it in order, you're gonna see the smallest, you're gonna see the largest very quickly, but otherwise you could just scan through it and keep comparing them.

The range was 18.

3.

So, hopefully you identified 19.

4 and 1.

1 and found the difference between them.

So, the last question where Laura had finished her homework and then that ink pen spoiled some of her answers.

What is missing? What has the ink covered up? So, on part A, largest number is what? The smallest number is 14, so the range is 10.

So if we know that the data runs from 14 and then goes up by 10 to get the other extreme, that means the largest number would be 24.

On part B, the largest number is 8.

The smallest number is unknown currently and the range is 12.

So, from 8 down by 12 you'll get to the smallest or the lowest, and that would be -4.

Part C in order.

<v ->3, -1, -1, 0, something, 6, 7, 10.

</v> So the range is 13.

Well, because this data is in order, we have the smallest and we have the largest, and the range is 13.

So, you could have put any number between zero and 6 in that place.

So for example, you could have gone for a 2.

You could have put zero.

You could have put 1, 2, 3, 4, 5 or 6 because that wouldn't change the order.

And therefore it wouldn't change the range.

Part D, any order.

So we've got 3, 5, 3, 7, 10, 12, 6, 8, something, and the range needs to be 11.

So, you have two options here.

You either went for a 1 or you went for 14.

So, if you went for 1 that was, you were keeping 12 as the largest and the range needed to be 11.

So that meant it had to go down to 1.

If you went for 14, you kept 3 as the smallest, added 11 to get your largest as 14.

No other numbers coulda been put there because otherwise the range would not have been 11.

We are now onto that second part of the lesson and that is thinking about the extreme values that we need for the range in different representations.

So, so far we've looked at lists of data and we've looked at dot plots.

So, we're gonna look at other types of representations of data and still considering where the range would be found.

Hopefully you've got an idea that the range now, because it is a measure of spread and it only includes the two extreme values, that very lowest, the smallest, and up to the largest value in the data.

So Jacob has said, "But is it necessary? Why do we have the range when we have the averages: mean, mode and median?" Sophia has responded to him and said, "Well, they are measures of central tendency, where the range is a measure of spread." So they are looking at, they are calculating different things ultimately.

Sophia is continuing with this idea with Jacob to try and identify why the range is important.

So the range only uses two values in a dataset.

We've looked at, you would've previously studied measures of central tendency, which are mean, mode and median or three of them are mean, mode and median.

So here Sophia's saying, "These four data sets all have a mean of 7." So, if you were to add them up and divide by how many there are, the answer would be 7 in every single case.

The mean is 7.

Jacob's quite surprised by that because he said, "They feel really different to each other though." And I'm in agreement with him.

That first one, 1, 1, 1, 1, 1, 43.

The mean is 7 but that data is so different from B.

B, the mean is 7, yes, they're all 7s.

And if we look at those data sets as dot plots, we've seen dot plots in the first part of the lesson.

It sort of shows them differences off.

That on part A, we've got all these really small values and then there's really, really large value.

On part B, they're all the same.

They're all stacked up on top of each other.

D, they're fit, they're evenly distributed across a place.

And C, there's a slight disparity between them but not too much.

And this is where the range is a really useful extra measure.

So it's not a measure of central tendency.

It's not trying to find a single value for the central data.

Instead it's trying to show you how varied data is.

So on A, the range is 42.

It goes from 43 to 1.

B, the range is zero, all the data is the same, and so the range is zero.

And that's always gonna be the case.

If you know that a data set has a range of zero, that means there is no variety, it's not spread out.

And so you would, that would imply to you that the data is all the same.

The value of the data is all the same.

C has got a range of 13.

9 and D has a range of 6.

So despite the fact that the mean value for all four of these data sets is equal, they've all got a mean of 7.

Their range shows that they are actually distributed very differently.

We can see that on a dot plot quite visually, but if we just work it out, you still can, you get the sense that this data is different.

We've got a line graph now as a different representation of data.

And it's a line graph showing the classroom temperature over the course of a day.

So the temperature of the classroom has been measured in degrees Celsius at 9:00 am, at 10:00 am, at 11:00 am, et cetera.

To calculate the range of the temperature, we need to identify where the two extreme values are and what they are.

So Lucas says, "That's gonna be the highest and lowest points." And so, that was at 1:00 pm the highest temperature, 21 degrees Celsius.

And in the morning at 9:00 am, the classroom was 15 degrees Celsius.

So, our range is 6 degrees.

The difference between the two extremes, which is the highest temperature and the lowest temperature.

And that's the change vertically on the line graph.

And that can be seen by that arrow.

A check for you then with a line graph.

What's the range time taken to travel to work? Pause the video whilst you find your two extremes and calculate the range.

Press play when you're ready to check your answer.

So, identify your two extreme points.

So the longest time taken was on Tuesday and that was 26 minutes.

The shortest time taken was on Friday and that was 18 minutes.

And so the difference, the range is 8 minutes.

And that is the difference between the highest point and the lowest point vertically on the line graph.

So, now we've got some data represented as a bar chart.

This bar chart isn't a frequency bar chart.

This bar chart is representing five data points.

So it's five pupils and their attendance marks.

So to find the range, we need to identify which student has the most attendance and which student has the lowest attendance.

So Lucas has got 26 marks, attendance marks, that's the most.

And Sam and Andeep both have 23, and that's the lowest attendance marks.

So, the range in the attendance marks for these five pupils is three marks.

It's not very varied.

And then, we've got a bar chart and a frequency table.

But this time, this bar chart is a frequency bar chart.

It represents the same thing as a frequency table.

So, here we've got data about how many sweets are in each pack of sweets.

So, imagine a small little sweets packet.

If you were to open many of them and count how many sweets you get in each packet, that's what this data is representing.

So, it's the same data on both the frequency table and this frequency bar chart.

So, what are the extreme values? This is where we need to really consider the context of the data.

The data is about the number of sweets per pack.

So the lowest amount of sweets in a pack is 7, the highest amount is 10, and they are the extreme values.

So on the frequency table, that's in the context column.

And on the bar chart, it's the horizontal labels on the bars.

So for the range for this data, if we were to look at it would be 3.

Some packs have as little as 7 sweets in them and some packs have as many as 10.

And so, the range of sweets per pack would be 3.

We've now got a bar chart that shows satisfaction score at a company.

It's a frequency bar chart.

So, the scores received range between 5 and zero.

So, they are extreme values.

Some people gave the company a satisfaction score of zero and some people gave this company a satisfaction score of 5.

So, the range is 5.

We've got another frequency bar chart and this data is about types of pets within one class, and it's being represented as a bar chart.

Andeep says he doesn't think that there are extreme values because the data is about pets.

Is he correct? Do we agree with him? Yes.

So, data that has no fixed order cannot have a range because we need to have a fixed order in order to know which one's the lowest and which one's the highest, which ones are our extremes.

And so the range is a measure of spread, but can only be calculated for numerical data or data that has an order.

A check for you.

True or false, and a justification.

So pause the video, read it through, make a decision on what you think is correct and then press play to check your answers.

It is false.

The range cannot be found on all bar charts.

And we saw that with the example of pets.

And the justification is that you cannot find range for qualitative data.

So, if it was data about colours, pets, food types, genres of music, you're not gonna be able to put them in an order to find extreme values.

So, you cannot calculate the range.

You're now gonna do some practise.

Question 1, which of these representations can you find the range? Pause the video whilst you decide.

You can always find the range for them as well if you wanted to.

But the question is about which ones can you find the range? Press play to come onto question 2.

Question 2 has got two bar charts where you can find the range, and that's exactly what you need to do for each question.

So find the range from the two bar charts.

Press pause whilst you have a go, and then when you're ready, press play.

Question 3 has got some data in a frequency table about wait times at a fast food restaurant.

And a local newspaper reported that customer's wait time ranged by 38 minutes.

Do you agree? So pause the video, analyse that data.

Has the reporter reported correctly.

And that is true for the data.

Or have they reported incorrectly? Pause the video, and then when you have finished, press play and we're gonna go through the answers to these three questions.

Question 1, as I said, you could have found the range as well if you wanted, but the question was about which of these reputations can you find the range? You can't find the range on the bar chart from A, because that data is qualitative and you wouldn't be able to put it in an order.

You can do it for B.

The data is about goals scored.

The frequency table on C, you can do, it's about shoe size.

And D, you can also find the range about the maximum temperatures.

Question 2, for each of the following bar charts, and they were bar charts where you could find the range.

You need to find the range.

So for part A, it was about number of cars and the range would be 4.

So, some households had no cars, some households had four cars.

So, there was a difference.

It was varied by that 4.

And on B, we've got single data points here.

So, carriage 1 had amount of occupied seats, carriage 2, et cetera.

So, we're looking at the difference from the most occupied carriage down to the least occupied carriage.

And so that is 37.

There is a range of 37 between carriage 1 and carriage 4.

Question 3, did the reporter report fairly and accurately about the wait time at this fast food restaurant? The answer is no.

So, the range of wait times is 7 minutes.

The longest wait time was 11, and the shortest was 4.

So the difference, how varied, how spread out is that data is only 7.

The reporter has reported the range of the frequency.

So, there was the highest frequency of 46 and the lowest frequency of 8.

The difference there is 38, but that's not about the wait time.

So, they've reported that incorrectly.

They've calculated the range incorrectly.

So, it's always about remembering the context that you're working in.

So, we finished the lesson about understanding and calculating the range.

The range is the difference between the two extreme values.

If it is qualitative data, then there will not be extreme values.

So, you cannot calculate the range.

The range is a measure of spread or dispersion.

So it's different to our averages, our measures of central tendency.

And it allows you to show how varied the values in the dataset are.

Dependent on what the diagram or the chart is, the type of it will dictate where the range is found.

The important part is identifying those extreme values, and then finding the difference between them.

Well done, and I hope you've enjoyed today's lesson.

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