Lesson video

Hi, everyone.

My name is Ms. Coe 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 today's lesson on histograms with equal bar widths.

It's under the unit graphical representations of data, cumulative frequency and histograms. And by the end of the lesson, you'll be able to construct bar charts for continuous data.

Let's have a look at some keywords.

We'll start with discrete data.

Discrete data is data that can only take distinct, specific values.

For example, shoe size or number of people.

We'll also be looking at continuous data.

And continuous data can take any value within a range.

For example, height, mass, or temperature.

We'll also be looking at the keyword histogram, and 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.

Today's lesson will be broken into two parts.

We'll be looking at constructing histograms with equal bar widths, and then moving on to interpreting histograms with equal bar widths.

So let's make a start looking at constructing histograms with equal bar widths.

Now, I want you to name as many different types of representations of data as you know.

Press pause.

I want you to write it down.

Great.

Let's see how you got on.

Well, there are so many.

Here's just a few.

How about pictograms or scatter graphs or stem and leaf diagrams or stacked bar charts, pie charts, bar charts.

There are just so many and we've just selected a few.

But what do all these data displays have in common? I've picked our pictogram, I've picked our bar chart, I've picked our stacked bar chart and I've picked a stem and leaf.

What do all these data displays have in common? Have a little think.

Well, they're displaying discrete data.

Izzy asks, "So how do we graphically represent continuous data? And there are quite a few different ways of displaying continuous data and a histogram is one.

So let's compare a bar chart and a histogram.

I want you to have a look at our two different displays of data.

What is the same and what is different? Have a little think.

Well, the one on the left is a histogram as it shows continuous data.

Time is continuous data.

The one on the right is a bar chart, and this bar chart shows discrete data.

And as you can see, the number of apps is discrete data and we know time is continuous data.

Now you might also notice there are gaps in our bar chart, indicating that the data is discrete.

However, with our histogram, there were no gaps, indicating that the data is continuous.

They are similar as they have equal length of bars and are plotted against the frequency.

So now let's have a look at some data.

An Oak teacher collects data from his 54 pupils on how long they spend on homework per week.

Oof, we've got a lot of data here.

Explain how you can sensibly display all this information.

Have a little think.

Well, a grouped table is a sensible display, given there are a lot of data.

So here's our data.

Which of the following grouped data tables would be an appropriate choice? And I want you to explain your reasoning.

Do you think it's table A or do you think it's table B? Press pause if you need more time.

Well done.

Let's see how you got on.

Well, table A doesn't really have that many classes.

There are a few classes and they do not allow a good snapshot of how the data is distributed.

Table B is a good choice.

The classes are all the same width and it's easier to see those comparisons.

Well done if you got this.

Now, the Oak teacher has put all the data from his 54 pupils into this table using equal class widths, showing how many hours per week each pupil spent on their homework.

Grouping the data using class widths makes it easier to read, especially if there is a lot of data.

Therefore, it's important to understand what the table is showing.

What I want you to do is have a look at this first row from our table.

Can you explain what this means? Well, it means there are six pupils who spend between zero and one hour a week on their homework, not including zero, but including that one.

What do you think the second row means? Well, it means there are eight pupils who spend between one and two hours a week on their homework, not including one, but we are including two.

What do you think this row means? Well, it means there are 14 pupils who spend between two and three hours a week on their homework, not including two, but including three.

It's so important to understand how the data is represented when using tables.

Let's have a look at a check.

Here's a frequency table showing the masses of parcels, but seven more pieces of data need to be added.

We have 11.

8, 12, 10, 3.

45, 5.

01, 19.

99, and 14.

989 where all of these values are in kilogrammes.

And what I want you to do is add the seven data values into this table and identify how many parcels have a mass greater than 10 kilogrammes.

So you can give it a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, the 3.

45 should have been in our first row, making the frequency 35.

We should have two extra values in our second row, the 10 and the 5.

01, making our frequency 12.

We should have three extra values in our third row to make a frequency of 15.

And lastly, we should have one more extra value in our last row to make our frequency 15.

So how many parcels have a mass greater than 10 kilogrammes? Well, there are 30 parcels with a mass greater than 10 kilogrammes.

Now, certain aspects of a histogram will be familiar.

The axes scale is increasing equally, equal bar width with the y-axis labelled frequency.

But the major difference between a bar chart and a histogram is there are no gaps unless there is no frequency for that bar.

Now let's draw a histogram showing the time pupils spend on their homework per week.

What do you think the x-axis should be? Have a little think.

Well, the x-axis has to be labelled as time and the x-axis can be labelled like this as it is increasing equally.

Alternatively, it can be labelled like this, as long as the x-axis scale is increasing equally.

I'm gonna leave it like this.

Now, what do you think our y-axis should be? Well, our y-axis should be the frequency.

So this is a sensible scale for the data in our table.

Now let's draw our histogram.

Here we have a bar with a width from zero to one hours and we know this has a frequency of six.

Next, the next row shows one to two hours.

So I've shown it here with a frequency of eight.

So now I have my bar.

Next, between two to three hours as shown here with a frequency of 14.

Then a bar width from three to four hours with a frequency of 14 and then a bar width from four to five showers with a frequency of 12.

Now it's time for your check.

Laura's drawn her histogram like this.

Do you think her histogram is a good display of data? Have a look and think.

Well, the x-axis shows clear bar widths, which are equal in length, but the scale of the y-axis makes it difficult to read the frequency of each bar.

Well done, everybody.

So now it's time for your check.

Here we have two histograms. Two Oak pupils constructed these histograms to display the data below.

Which is the correct chart? And I want you to explain why the other is incorrect.

<v ->So you can give it a go.

Press pause for more time.

</v> Well done.

Let's move on to question two.

Question two wants you to draw a histogram showing these lengths of different pieces of string.

So you can give it a go.

Press pause one more time.

Well done.

Let's move on to question three.

Question three wants us to draw a histogram, showing the time it takes to complete a puzzle cube.

Give it a go.

Press pause if you need more time.

Great work.

Let's go through these answers.

Well, here's our answer to question one.

A would be an incorrect choice because the pupils combine two of the class groups to create one group.

In other words, 10 less than W, less than or equal to 15 and 15 less than W, less than equal or to 20 have been combined.

Question two, your histogram should look like this.

And remember, as long as you've chosen an appropriate scale with the X scale increasing equally and the Y scale increasing equally, that's important.

For question three, here's my example of my histogram.

Once again, as you can see, this is a nice example because I have a nice clear X scale and a nice clear y scale.

Great work, everybody.

Now it's time for interpreting histograms with equal bar width.

Now, understanding the table and histogram allows you to extract the necessary information.

This histogram shows the time pupils spent in the lunch queue.

And Andeep says 35% of students waited more than 10 minutes.

Is he correct? Well, let's have a look.

Let's work out how many pupils there were in total.

Well, to do this, we work out the frequency from each bar.

How many pupils were there? Well, all you have to do is identify the frequency from each bar.

Between zero and two minutes has a frequency of five.

Between two and four minutes has a frequency of five.

Between four and six minutes has a frequency of seven.

Between six and eight minutes has a frequency of six.

Between eight and 10 minutes has a frequency of six.

Between 10 and 12 minutes has a frequency of seven.

Between 12 and 14 minutes has a frequency of three.

Between 14 and 16 minutes has a frequency of five.

Between 16 and 18 minutes has a frequency of five.

And lastly, between 18 and 20 minutes has a frequency of one.

So how many pupils were there? Have a little think.

Press pause if you need more time.

Well, there were 50.

So if we know where there were 50, how many people waited more than 10 minutes? Have a little think.

Press pause if you need more time.

Adding this up, it's 21.

So is 21 pupils out of 50 pupils the same as 35% of 50? No, it's not, so Andeep is wrong.

42% of pupils were waiting more than 10 minutes in the queue.

Now it's time for your check.

A puzzle cube competition was launched and pupils qualify for the next round if they can complete the puzzle cube in no more than 20 seconds.

What percentage of pupils moved on to the next round? Have a little think.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, identifying the frequencies, I have my frequencies labelled here.

This identifies the number of people who completed the puzzle cube in less than 20 seconds.

So it's eight out of 20, which is 40% who qualify.

Well done if you got this.

Great work, everybody.

So now it's time for your task.

What I want you to do is fill in the table using the information from the histogram.

The histogram shows masses of parcels in kilogrammes.

Take your time and press pause if you need.

Well done.

Let's move on to question two.

Question two wants you to fill in the information using the table and histogram.

It's the time to complete a puzzle.

You might notice we're missing some information from our table and we're missing some information from our histogram.

Have a little think, read the question carefully.

Interpret that histogram and interpret that table carefully so you can answer the question.

Give it a go.

Press pause if you need more time.

Well done.

Let's move on to question three.

Question three shows the histogram shows the lengths of some boxes.

I want you to show, with working, if the following are true or false.

50% of the data is 20 centimetres or less.

I want you to show with working if this is true or false.

Press pause if you need more time.

Well done.

I have to have a look at B.

5% of the data is greater than 45 centimetres.

What do you think.

True or false? Show your working.

Press pause if you need more time.

Great work.

Let's move on to these answers.

Well, hopefully you've completed the table using our histogram.

30 less than W, less than or equal to 40 should have a frequency of 13.

Next, 40 less than W, less than or equal to 50 should have a frequency of seven.

50 less than W, less than or equal to 60 should have a frequency of 11.

Next, 60 less than W, less than or equal to 70 should have a frequency of 14.

Lastly, 70, less than W, less than or equal to 80 should have a frequency of five.

Well done if you got this.

Next, this was a great question.

You had to use the histogram to fill in the table and you had to use the table to fill in the histogram.

Very well done if you got these frequencies.

Five, six, three, four and two.

And well done if you got the correct height of our histogram with equal bar widths.

For question three, let's see how you got on.

Well, firstly, it was important to identify the frequency from each bar.

So I've labelled it here, 6, 15, 6, 9, and 4.

Now, the first statement is false because 52.

5% of the data is 20 centimetres or less.

Really well done if you got this.

The second statement is hard to tell.

Assuming that there's an equal distribution of the frequencies in each bar, then it would be true.

Well done if you got that.

That was a tough one.

Great work, everybody.

So in summary, a histogram is a way of graphically representing continuous data and 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.

Really well done, everybody.

It was wonderful learning with you.

I hope you enjoyed looking at this wonderful display of continuous data as it's used so much.