Lesson video

Hi, everyone.

My name is Ms. Ku, and I'm really excited to be learning with you today because today we're looking at histograms under the unit of graphical representations of data.

Hope you enjoy the lesson.

Let's make a start.

Hi, everyone, and welcome to this lesson on constructing histograms and box plots using technology, under the unit graphical representations of data, cumulative frequency and histograms. By the end of the lesson, you'll be able to construct histograms and box plots utilising technology.

So let's have a look at some key words.

A histogram is a diagram consisting of rectangles whose area is proportional to the frequency in each class and whose width is equal to the class interval.

And a box plot is a diagram that clearly shows the minimum and maximum value of a data set along with the three quartiles.

Today's lesson will be broken into two parts.

We'll be looking at constructing histograms in Desmos first, and then constructing box plots in Desmos.

So let's make a start, constructing histograms in Desmos.

Drawing a graphical representation of a dataset can be time consuming, and for large datasets, the likelihood of making an error is very high.

Luckily, software exists that can make this task significantly easier.

One graphing platform allows you to import data and choose the graphical representation is Desmos.

So firstly, type in https://www.

desmos.

com/calculator, or simply click this link Desmos and it'll open up a blank graph.

If you find during the lesson you want to press pause at any time, please do just to make sure what I have on the screen matches what you are doing.

Now in your Desmos graph, I want you to type in histogram, and then an open curly bracket.

and Desmos will now ask you something.

Desmos is now asking for the data set and the class width.

In other words, they call it the bin width.

So now it's time to input some data.

Here we have a list showing the times it takes 30 pupils to tie their shoelaces.

And the data is also available in this spreadsheet available in this link.

You can either copy and paste the data from the spreadsheet.

In other words, select column A, press Control + C, then return to Desmos, click next to the open bracket in row one and press Control + V to paste.

Or if you want to do this, you can type in each value into Desmos, but make sure you separate each data value with a comma.

I know what I'd to prefer as I like to be more efficient.

So the start of row one should now look like this, histogram with an open curly bracket, and then we have an open square bracket where the data has now been inserted.

The end of the row should look like this.

The end of the data value is ended with a square bracket.

Make sure the square bracket is closed at the end of the list so Desmos knows all the data is in there.

And the comma is there to show the class width, which we'll look at next.

The bin width is the width of each class.

So we're drawing a histogram with equal class widths first, and in this case, the class width is two.

So simply type two and close the bracket.

So it should look like this.

I want you to press Enter to draw the histogram, but you might notice you can't see the graph.

So to see the graph, click the magnifying glass to zoom into the graph.

Now the histogram is seen.

And the histogram may look good, but it's not finished yet.

At the moment, the bars are drawn with the centre of each bar at the starting value of each class.

For example, the first bar is for the class between 12 less than the time, less than or equal to 14.

To correct this, you have to select Left for the bin alignment.

So you can see it here.

Clicking on the spanner also allows you to assign labels to the axes.

So let's label, the x-axis is the time it took to tie the shoelaces.

So let's label it Time (seconds).

The y-axis is the frequency.

So let's label it Frequency.

And remember, we did not need to calculate the frequency density as the class widths are the same.

So you can continue to play around with the settings in order to change the appearance of the histogram if you wish, but for me, this is a very nice and clean histogram showing the distribution of the data where our histogram has equal class widths.

Well done if you got this.

So let's have a look at a check.

To input data into the Desmos, you can either type the data into Desmos, take a screenshot of the data and paste it into Desmos, or copy and paste the data into Desmos.

What do you think? Well, it should be A and C.

You can either type the data into Desmos or just copy and paste the data into Desmos.

So now let's construct a histogram with unequal class widths.

And this is easily done with a template, but it is important to understand what the template does with the data.

It will load a template of a histogram.

So let's understand the basics of these settings and functions.

First of all, the template explains how you'll enter the upper and lower bound for each class.

Although there are no class intervals seen here in the frequency table, they do exist, but they're represented differently in Desmos.

Here it states we have a frequency of four for a class width of zero less than X, less than or equal to 10.

The lower interval value is set as zero as the upper interval value is indicated in the table.

Here, a frequency of eight for a class width of 10 less than X less than or equal to 15 is indicated here.

The lower value is set as 10 and the upper interval value is indicated in the table.

Here we have a frequency of 20 for a class of 15 less than X less than or equal to 20.

The lower interval value is set as 15 and the upper interval value is indicated in the table.

So identify the class intervals and frequencies indicated in this frequency table.

Press pause as you'll need more time.

Well, the frequency of 16 is indicated here for a class of 20 less than X, less than or equal to 30.

And here we have a frequency of five for a class of 30 less than X, less than or equal to 50.

Now we understand how Desmos represents the class intervals and frequencies.

You can see we have unequal class width plotted against the frequency density, and Desmos has calculated all this for us.

So now let's insert our own group data and create a histogram with unequal class intervals.

Here we have the times to complete a puzzle, and what we're going to do is we're going to put this information into Desmos.

So go to the frequency table in Desmos and insert the upper time interval of the first class.

We're gonna change this to 15.

Next, we're going to change the frequency to five.

So it should look something like this in Desmos.

Now you've told Desmos we have a class interval of zero less than T, less than or equal to 15 with a frequency of five.

Next, let's go to the next row in Desmos and insert the upper time and the next interval.

Here, we're gonna change it to 35 as this is our upper time interval, and we're gonna change the frequency to 14.

So it should look like this.

So now you've told Desmos we have a class interval of 15 less than T, less than or equal to 35 with a frequency of 14.

So now let's move on to a check.

I want you to finish inputting all the intervals and frequencies into the histogram and put the following settings in as well.

So use that little spanner.

I want you to make the font large.

I want you to label the x-axis time and then S.

Label the y-axis as frequency density.

And I want you to change the x-axis visible from negative two less than or equal to X, less than equal to 70 with step to 10.

And have the y-axis visible from negative 0.

5 less than or equal to Y, less than or equal to five with steps of one.

You'll see all these wonderful settings when you press that spanner tool.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, the setting should look like this and the table in Desmos should look like this, and your histogram should look something like this.

Really well done if you've got this.

Great work, everybody.

So now it's time for your task.

Either copying from the data here or typing the data in, draw a histogram in Desmos showing Oak Class B's time to tie their shoelaces with the following settings, equal class widths with bin width of two.

Label the x-axis as time in seconds.

Label the y-axis as frequency.

And have the x-axis visible from 10 less than or equal to X, less than or equal to 25 with step of 5.

And have the y-axis visible from negative one less than y, less than or equal to 12 with steps of 2.

Press pause as you'll definitely need more time.

Well done.

Let's have a look at question two.

Draw the histogram using this template with the following settings and using this frequency table.

Make the font large, label the x-axis as mass kilogrammes.

Label the y-axis as frequency density.

Have the x-axis visible from negative two less than or equal to X, less than or equal to 60 with steps of 5.

And have the y-axis visible from negative 0.

2 less than or equal to Y, less than or equal to four with steps of one.

Give it a go.

Press pause if you need more time.

Well done.

Let's move on to question three.

Using the template given here and these settings, make the font large, label the x-axis as time in seconds, label the y-axis as frequency density.

Have the x-axis visible from negative 0.

2 less than or equal to X, less than or equal to five with steps of one.

And have the y-axis visible from negative two less than or equal to Y, less than or equal to 30 with steps of 10.

And I want you to draw the histogram of this frequency table.

So you can give it a go.

Press pause if you need more time.

Well done.

Let's go through these answers.

Well, for question one, we should have had this wonderful, beautiful histogram.

Well done if you got this.

If at all you want to press pause at any time, please do just to make sure what I have on the screen matches what you are doing.

For question two, you'd had this fabulous histogram.

If at all you want to press pause at any time, please do just to make sure what I have on the screen matches what you are doing.

Good work if you got this.

And for question three, you should have this fantastic histogram.

Well done if you got this.

Well done, everybody.

So now well, let's look at constructing box plots in Desmos.

Constructing box plots is a very similar process.

So let's insert Oak Class A group data, which is found here on how long it took them to tie shoelaces.

Well, same again, you need to open Desmos, type in box plot and then enter or paste the data from class A.

And it should look something like this.

What you might notice is nothing has happened yet.

So pressing the zoom fit or that little magnifying glass will show that box plot.

So let's have a look at these words, offset.

Now what I want you to do is change the offset by choosing different values.

I want you to notice what's happening to the box plot.

For example, I've changed it to two, originally it was one, now I'm changing it to three.

What do you notice when I change the offset value? Have a little think.

Well, the offset value moves the box plot from the x-axis, and the larger the offset value, the further the box plot from the x-axis.

So now let's have a look at height.

I want you to change the value of the height by choosing different values and make an observation.

What happens? So for example, I've changed the height to 1.

5, I've changed the height to two.

What happens as we change the height? Well, hopefully you spot the height changes the height of the box, which represents the interquartile range.

In addition, when presenting box plots, it's nice to change the colour and remove the y-axis so the representation is cleaner.

And to do this, to change the colour, simply keep your finger pressed on the mouse over the coloured box plot.

Some colours will pop up, and simply pick the colour that you want.

So here I've picked a lovely pretty purple.

If at all you want to press pause at any time, please do just to make sure what I have on the screen matches what you are doing.

Now to make the y-axis invisible, go to that spanner again.

In other words, settings and unclick the y-axis box.

And what you'll notice is we have now made our y-axis invisible.

So let's have a look at a check.

To change the position of the box plot, you should what? Change the value of the height, change the value of offset, or change the y-axis? See if you can give it a go.

Press pause if you need more time.

Well, hope you spotted it's the value of the offset.

Great work, everybody.

So now it's time for your task.

Either by copying the data from here, this link or typing in the data, draw a box plot in Desmos showing Oak Class C times to tie shoelaces using the following settings.

I want you to make the font large.

Draw a black box plot.

Make the offset 1.

5.

Make the height one.

Label the x-axis as time in seconds.

Make the y-axis invisible.

Have the x-axis visible from 15 less than or equal to X, less than or equal to 25 with steps of 1.

And have the y-axis invisible from negative one less than or equal to Y, less than or equal to four with steps of one.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's have a look at question two.

Question two gives you these data sets.

We have A has a data set of 1, 1, 2, 2, 2, 3, 3, 3, 4, and 4.

B has a data set of 1, 2, 2, 2, 3, 3, 4, 4, 4, and 5.

And C has a data set of 2, 2, 3, 3, 3, 4, 4, 4, 4 and 5.

And I want you to draw three box plots where dataset A is displayed in blue, dataset B is displayed in orange, dataset C is displayed in black.

The x-axis is labelled mass in kilogrammes.

The height of each box is one, and there are two units squares difference between each box plot, and the box plots are seen with the x-axis visible from negative 0.

5 less than or equal to X, less than or equal to six with steps of one, and an invisible y-axis from negative one less than or equal to Y, less than or equal to five with steps of one.

Great question.

See if you can give it a go.

Great work, everybody.

So let's have a look at these answers.

Well, for question one it should have looked something like this.

Really well done if you got this.

Press pause if you need.

Well done.

For question two, it should have looked like this.

Massive well done if you've got this question.

Press pause if you need.

Well done, everybody.

So in summary, Desmos allows you to quickly represent data in a variety of ways.

It's important to know how to change settings using that spanner tool.

Great work, everybody.

Have a little play with Desmos, it's amazing, and I hope you enjoyed the lesson.

Well done.