Lesson video

Hello, my name's Miss Parnham.

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

We can use a histogram in order to find an estimate for the median and interquartile range of a frequency distribution.

The way that we do that is we work out the total frequency.

That's a case of adding up the frequencies represented by each bar, which is the area of each bar.

We find the area by multiplying the class width by the frequency density.

The width by the height of each rectangle.

So, here we have six, 14, 13, and three.

Adding those four numbers together gives us a total frequency of 36.

So, if we have 36 values, then the 18th value will be the median.

So, let's go back to our bars and see that the first group contains six, so we add 14 on.

That gets us to 20.

That's past 18.

So, the median must be somewhere in this second group of five to 10.

We can estimate the value of the median by working out how far in the group the median is.

So, if it's the 18th value, this is 12 more than where we were when we looked at the first group.

So, we had six in the first group, so it's another 12 values past that.

So, it's 12/14 of the way through this group.

We're multiplying by five because that's the class width.

So, it will be 4.

29 past five.

So, five added to 4.

29.

So, the estimate for the median is 9.

29 kilometres.

Right.

The interquartile range is worked out in a very similar way.

Again, we have a total frequency of 36.

1/4 of this is nine, so we need to work out where the ninth value is.

So, we have six in that first category.

So, that's another three.

So, we need 3/14 of five, which is 1.

07.

So, we are 1.

07 above five.

So, this gives us a lower quartile of 6.

07.

Now, on the upper quartile, we need to be nine below the total of 36.

So, if you look at the final category, that contains three.

So, it's 6/13 from below 20.

So, let's put our line there and go 6/13, which is 4.

62 below 20.

This gives us an upper quartile of 15.

38.

The difference between the upper and lower quartiles is the interquartile range.

So, we have an interquartile range of 9.

31 kilometres.

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.

This question is broken down into steps to help you estimate the median.

So, once we have a total frequency of 50, which we found from adding up all the areas of the bars, we know that the median is the 25th value.

So, going back to the diagram and adding up the areas of the bars until we get to the 25th value or past it, gets us, obviously one, then four, then adding the 12 on gives us 16, and then adding 15 on gives us 31.

So, we've gone past the 25th value, so the median is somewhere in the category 20 to 30.

Now, to estimate the median itself, we go back to the total that we had before we had 31, which was 16.

We would need nine more to get to the 25th value.

So, we're 9/15 of the way through that category of 20 to 30.

So, 9/15 is 3/5.

So, we're 3/5 of the way between 20 and 30.

Now, that's a gap of 10.

So, 3/5 of 10 is six.

So, we're six minutes after 20, so that's where 26 minutes comes from.

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.

50 is halfway through the group of 40 to 60.

So, estimating those that are over 50, means adding together half of the frequency for that group.

So, half of 16 added onto 18 and 10, the frequencies from the two subsequent groups.

And that will give you that estimate of 36.

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.

We have a total frequency of 48.

So, the 24th value is the median.

This is 2/18 of the way between five and 10, and hence we've got an answer that we've had to round to three significant figures.

The lower quartile is the 12th value, which is 1/3 of the way between two and five.

So, it's one bigger than two or three.

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, for the interquartile range, we need to subtract the lower quartile from the upper quartile.

So, with a total frequency of 80, then these are the 20th and 60th values, respectively.

That's all for this lesson.

Thank you for watching.