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Hello, my name's Ms. Parnham.

In this lesson, we're going to learn how to find probabilities from a histogram.

We can use histograms to work out frequencies, and those frequencies can be used to find probabilities.

So the first thing we're going to do is work out the frequency represented by each bar.

That's the class width multiplied by the frequency density, which is the height.

So we have 6, 14, 13 and 3, and adding those together gives us a total frequency of 36.

So any probabilities that we find, are fractions of 36.

We're being asked what's the probability that a person chosen at random, cycled less than 10 kilometres.

So we can see the 10 kilometre mark as two bars below it.

So let's add those two together.

6 add 14 equals 20, so the probability is 20/36.

You can simplify that fraction if you want.

Well, you don't have to.

The next question asks us what's the probability that a person chosen at random has cycled between 15 and 25 kilometres? We handle this a little bit differently because those numbers are not the upper or lower bounds of groups.

So let's put two lines on our histogram so that we can see where they are.

So assuming that within those groups, the data is evenly distributed.

We would take half of the 10 to 20 group, half of the 20 to 30 group, add them together for a total, and this will give us the numerator on our fraction of 36, which is the denominator.

So that's 6.

5 plus 1.

5, which is 8.

So we estimate that 8/36 or any simplified fraction which is equivalent to this, is the probability that a person chosen at random has cycled between 15 and 25 kilometres.

Here's a question for you to try it.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

We have a total frequency of a 100 because we've added of all the areas of the bars.

And the number of plants under 20 centimetres, can be found by adding together 16 and 24, which gives us 40.

So you can give probability as any fraction, decimal or percentage.

If you have a different fraction to 2/5, then anything that's equivalent to it, you can still mark correct.

Here's another question for you to try it.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

The total frequency is 50, and adding together 13 and 6 gives you the total people who took more than 30 minutes to solve this puzzle.

And as before, we can express this as a fraction, decimal or percentage, so any equivalent fraction to 19/50 is can also be marked right.

In this example, we're going to have to find the scale on the vertical axis before we can find the frequencies represented by each bar.

The only clue we have is that 12 people took less than 10 minutes to solve a puzzle.

So we know that the first bar has an area of 12.

Now, it has a width of 10, so it must have a height of 1.

2.

So this is 12 tiny squares.

So each tiny square is not quite 1, so each increment of the side is not.

5.

So we can put the scale on.

Every second increment is 1.

So now we can work out the heights of all these bars.

Multiply by the class width to find the frequencies.

We have 12, 14, 23, 17 and 22.

That gives us a total frequency of 100.

So when we work out a probability, the denominator on the fraction will be 100.

We are asked to estimate the probability that a person picked at random took more than 50 minutes to solve the puzzle.

So 50 is in the middle of the last category of 40 to 60.

And we assume that they're equally distributed, so we have 22.

This gives us 11/100.

This is the probability that a person picked at random took more than 50 minutes to solve the puzzle.

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.

Because the frequency of the 60 to 70 group is 28, and the class width is 10, then that means the height of that bar is 2.

8.

And then that helps you to complete the scale on the vertical axis.

And then you can find the areas of all the other bars.

I'm giving you a total frequency of a 100.

We then need to estimate many people are aged between 30 and 50, which are both values in the middle of two separate groups.

So we need to add together half the frequency of the 20 to 40 group with half the frequency of the 40 to 60 group.

This gives us 9 plus 12, which is 21.

So we have 21/100 or the equivalent decimal or percentage.

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.

We know the fist bar represents 10 people.

And with the class width of 10, means the height is 1.

That will help us complete the scale on the vertical axis, and then, subsequently find all the areas of the other bars.

So we need a person who is chosen at random, what's the probability their aged between 30 and 50? We need to take half of 19 and add it to 12, and then divide this by 80.

So we get 0.

269 as a decimal, or the equivalent percentage or fraction.

That's all for this lesson.

Thank you for watching.