Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to be calculating the mean of certain numbers that are displayed in a group frequency table.

Here are some times it took 20 students to walk to school.

The times are given in minutes.

Why can't we work out the mean exactly? It is because we do not know the exact amount of time that it took each of the 20 students to walk to school.

This means that we're going to find an estimate for the mean.

To do this, We're going to write down the midpoint of each of the classes.

This means the middle of the values in the first column.

The middle of one and five is three, Midpoint of six and 10 is eight, 11 and 15 gives a midpoint of 13 and 16 to 25 gives a midpoint if 20.

5.

Next we're going to multiply the frequency by the midpoints.

Here I've written frequency multiplied by time.

This gives us these times.

The total of each of these times is 202.

5 minutes.

To calculate the mean, we're going to divide the total by the number of items. In this example, we're going to divide 202.

5 by 20.

The estimate for the mean is 10.

1.

This has been rounded to three significant figures.

Here is some lengths of some goldfish.

Inequality symbols have been used to group the data.

The first group of data is that any goldfish that have got a length that is greater than 10 millimetres, but less than or equal to 30 millimetres.

Let's start by finding the midpoint of the length.

This is called midpoint of each of the classes.

The classes are the groups of lengths.

The first midpoint is 20 millimetres then 35, 45 and 70.

Next we're going to multiply together the frequency and the midpoint.

I've called this the length.

we're then going to add together these lengths.

So the total length of all of the goldfish is 1295 millimetres.

This is 30 goldfish.

The mean is found by dividing the total length by the number of items. In this example, this is 1295 divided by 30.

The estimate for the mean length of this 30 goldfish is 43.

2.

This has been rounded to three significant figures.

What do you think the modal class is? This is the grouping that has got the highest frequency.

In this example, it is 40 to 50 millimetres.

Here is a question for you to try.

Pause the video to complete your task I will resume once you're finished.

Here are the answers.

The sum of the midpoints multiplied by frequency is 97.

5.

The sum of the frequencies is 15.

The calculation you need to do to find the estimate for the mean is 97.

5 divided by 15, which gives an answer of 6.

5 minutes.

Here's a question for you to try.

Pause the video to complete your task I will resume once you're finished.

Here are the answers, the sum of the midpoint multiplied by the frequency is 260.

The total of the frequency is 20.

The calculation that you need to do to find the estimate for the mean is 260 divided by 20 which gives you an answer of 13 grammes.

What mistake has been made here? They have divided by the wrong number.

Need to find the total of the frequencies and divide by this.

Here are some questions for you to try.

Pause the video to complete your task I will resume once you're finished.

Here are the answers Rob has divided by the sum of the midpoint rather than the sum of the frequencies.

The correct answer is 53.

5 centimetres.

Here are some questions for you to try.

Pause the video to complete your task I will resume once you're finished.

Here are the answers.

The estimate for the mean length of the flight is 4.

075 hours.

65% of the flights were less than or equal to five hours.

That's all for this lesson.

Thanks for watching.