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Hello, my name is Ms. Parnham.

In this lesson, we're going to learn how to plot a histogram.

When we put data into groups, those groups do not have to be the same size.

If we have data cluster around a particular area, we may wish to use narrower groups.

Let's look at this example to illustrate the point.

So it shows the distance between home and workplace of 60 employees.

The first group is five wide because it goes from nought to five.

So the difference between nought and five is five, so the class width is five.

The second group has that lower bound of five and an upper bound of 10, so as a class with a five, because that's the difference between five and 10.

So if we find the difference between the lower bound and upper bound of the next three classes, that gives us 10, 10, and 20.

We're going to draw a histogram, which looks similar to a frequency diagram, but because we've got these different class widths, if we drew it using frequency, we would have a misleading diagram because those with wider class widths would have much bigger bars.

So we must calculate frequency density.

Frequency density is frequency divided by class width.

So the frequency density for the first category is 2.

4, because this is 12 divided by five.

And then we do 15 divided by five to get three, 18 divided by 10 gives us 1.

8, 11 divided by 10 is 1.

1 and four divided by 20 is 0.

2.

So when we plot a histogram, we will plot the distance against the frequency density.

The first bar goes between nought and five and it's 2.

4 height.

The second bar goes between five and 10 and its three high.

The next one goes between 10 and 20 and is 1.

8 high, 20 to 30 and 1.

1 high 30 to 50 and 0.

2 high, and this is a histogram.

In a histogram, the frequency is the area of the bar, because if we multiply the height, which is the frequency density by the class width, this gives us the frequency.

Here's a question for you to try, pause the video, to complete the task and restart the video when you're finished.

Here are the answers, the modal class interval, just means which class interval or group is the mode.

So looking at the table, the highest frequency we have is 15, and this relates to the group of 15 to 20.

So the modal class interval is 15 to 20.

Here's another question for you to try, pause the video, to complete the task and restart the video when you're finished.

Here are the answers, Mo has actually drawn a frequency diagram here because he's plotted frequency on the vertical axis rather than frequency density.

But unfortunately his diagram is quite misleading.

If you look at the table, the modal class interval is 10 to 20, whereas on the histogram, this seems completely dominated by the third and fourth class intervals.

This is because they have a wider class width.

Here's a further question for you to try, pause the video, to complete the task and restart the video when you're finished.

Here are the answers, always make sure you read the scale on the vertical axis carefully.

You frequently have to draw bars that have heights, which are decimals and it can be different every time, sometimes the smaller increments can be maybe 0.

1, 0.

2, 0.

5 so you need to check question to question.

Here's another question for you to try, pause the video, to complete the task and restart the video when you're finished.

Here are the answers, remember that the frequency is the area of the bar.

So for example, the bar for the fourth group is three times bigger than the bar from the first group.

That's all for this lesson.

Thank you for watching.