Lesson video

Hi, I'm Mrs. Wheelhouse, and welcome to our series of lessons on how to use your Casio calculator.

In these lessons, we're looking at three of the Casio calculator models, so let's get started.

By the end of today's lesson, you'll be able to use the fx-991CW to perform calculations with data.

On the screen, you can see some keywords we're gonna be using in our lesson today.

Feel free to pause the video now and have a read through them.

And here are some more that we're going to be using.

Again, feel free to pause the video so you can read through them.

Our lesson is broken into two parts.

Let's begin by finding the mean from a frequency table.

The arithmetic mean for a set of numerical data is the sum of the values divided by the number of values.

"So does this mean, says Izzy, "That I need to use the calculate mode to add all the numbers before dividing?" And Jun says, "There's an easier way to calculate the mean." In this lesson, we'll be using the Casio fx-991CW model.

We'll cover how to use this calculator to carry out different calculations.

After switching the calculator on, you will see this screen.

You can use the arrow keys to navigate between the options.

We're going to begin by focusing on how to calculate the mean from a frequency table.

So navigate to Statistics and press the Execute button.

Here is a table showing the number of diners at various tables in a restaurant.

This represents three tables, each with four diners, and this represents two tables, each with five diners.

We're dealing with one set of data, so we choose one variable from the statistics menu.

We now need to put the values from the table into the calculator.

If the frequency column is missing, press Tools, select Frequency, and then select On.

Please enter zero and then press Execute.

What value appears in the frequency column? Pause and do this now.

You should have seen that the value one appears.

This is because one is the default frequency value.

You can change the value by navigating to the value you wish to change and then typing the correct value and pressing Execute.

It's now time to enter the remaining values into the calculator.

Pause and do this now.

Welcome back.

Pressing the down arrow key will let you see the rest of the table and you should have what you can see now on the screen.

Once all the value have been correctly entered, you press Execute.

Press Execute again to generate the mean for the data you entered.

The mean is written as x with a bar across the top.

What is the value of the mean? Well done if you said three.

Izzy says, "Well, hang on, but what if I have a grouped frequency table?" And Jun says, "Well, your calculator can still find an estimate for the mean." Now, to quickly clear all existing data in the table, you can press Tools, then select Edit and Delete All.

You'll then have a blank table to put the new values into.

Alternatively, you can just overwrite the existing values.

Here's a group frequency table.

57 people were surveyed and asked how much money they spent on food during their visit to Oakfield Supermarket.

To calculate an estimate for the mean, we need to use the midpoint for each class.

The calculator can do this for you.

So we enter the calculation that we would use to find the midpoint and then press Execute.

So here we're going to add the zero, the bottom of the class, to 20, the top of the class, and then divide the result by two.

It's really important you use the parentheses or the brackets here so that your calculator knows the order to carry out these operations in.

When you press Execute, the midpoint is displayed in the first column.

So the midpoint for the first class is 10.

It's now your turn.

Calculate an estimate please for the mean amount spent per visitor.

Pause the video and do this now.

Welcome back.

You should have found that 68 pounds and 25 pence is the estimated mean amount spent per visitor.

Remember, you needed to use the midpoints and you needed to enter the correct frequencies.

It's time for your first task.

Question one.

This frequency table shows the number of goals scored in each match by all the teams in a club over one football season.

What was the mean number of goals scored? Pause the video and work this out now.

Question two.

This frequency table shows the star rating received by a restaurant over its opening weekend.

What was the mean star rating? Pause the video and work this out now.

Question three.

The frequency table shows the number of bedrooms in different houses within an area of town.

What is the mean number of bedrooms? Pause and work this out now.

Question four.

The time it takes for a sample of pupils to travel to school is collected in this grouped frequency table.

What is the estimated mean travel time to the nearest minute? Pause and work this out now.

Welcome back.

It's time to go through our answers.

For question one, the mean number of goal scored was 1.

65, which you could, of course, have rounded to two.

Question two.

The mean star rating was 3.

64 et cetera stars, which rounds to four.

Question three.

The mean number of bedrooms was 2.

5, which rounds to three.

And then question four, the estimated mean travel time to the nearest minute is 18 minutes.

Well done if you've got this all right.

I hope you found that using the calculator made calculating the mean significantly faster.

It's time for the second part of our lesson.

We're gonna be looking at doing some analysis.

Izzy says, "Well, when I found the mean, there was lots more shown on the screen." And Jun says, "That's because other calculations are performed at the same time." So let's look at this example again.

We have a table showing the number of diners at various tables in a restaurant.

When we calculated the mean, this information was displayed.

Pressing the down arrow key reveals more information.

This is on the second page and this is on the final one.

We're gonna consider the information needed for our GCSE maths, so there's more here than we need for the GCSE.

And in fact, if you consider going on to do maths after your GCSE, you'll be using more of this information.

The top gives us the mean.

The sum of x is the sum of the values.

On the second page, we have n, which is the number of values.

The minimum x value, which was zero.

The lower quartile, the median, the upper quartile, and on the final page, the maximum value for x.

Let's do a quick check.

For this data, please calculate the mean, the median, and the interquartile range.

Remember, the interquartile range can be found by taking the upper quartile and subtracting the lower quartile from it.

Pause and work on this now.

Welcome back.

We should have found that the mean is three, the median is three, and the interquartile range is four subtract two, which is two.

It's now time for our final task.

Question one.

This frequency table shows the number of goals scored in each match by all the teams in a club over one football season.

Part A, calculate the median.

Part B, calculate the interquartile range.

And part C, would the club prefer to report the mean or median as the average number of goals scored and why? Pause the video while you work on this now.

Question two.

This frequency table shows the star rating received by a restaurant over its opening weekend.

Part A, calculate the median.

Part B, calculate the interquartile range.

And part C, would the restaurant prefer to report the mean or median as the average rating and why? Pause and work on this now.

Question three.

The frequency table shows the number of bedrooms in different houses within an area of a town.

A developer wishes is to build more expensive houses, three or more bedrooms, but the local council want cheaper housing.

The council argued that there are already enough houses with three or more bedrooms. Are the council correct? Use the data to support your decision.

Pause the video and work on this now.

Question four.

The time it takes for a sample of pupils to travel to school is collected in this grouped frequency table.

It takes 17 minutes for Jacob to travel to school by bus.

Jacob claims that this takes him longer than the average pupil, so he should be taken to school by car every day instead.

Do you agree or disagree with Jacob? Use evidence to support your answer.

Pause the video and do this now.

Welcome back.

Let's go through the answers.

Part A, the median is one goal.

Part B, the interquartile range is two goals.

And part C, would the club prefer to report the mean or median as their average number of goals scored? Remember the mean was 1.

65 and the median is one.

I personally think the club would prefer to report the mean as it rounds to two goals, making the club's performance look better.

Well done if you said something similar.

Question two.

The median rating was four stars and the interquartile range was two stars.

Now, the restaurant can report either the mean or the median because the mean rounds to four stars and the median is four stars.

I've pointed out that by reporting the median, they didn't have to do any rounding at all, so that's slightly better.

Well done if you said something similar.

Question three.

Are the council correct that there are enough houses with three or more bedrooms? Well, the mean number of bedrooms is 2.

5, the median is two, and the interquartile range was one.

Here's an example of what you could have put.

I've said, well, if the council uses the mean, then they can round and state that the average number of bedrooms in houses in this area is three.

Therefore, there are plenty of houses with three or more bedrooms in.

Question four.

So did you agree or disagree with Jacob? Well, the mean is approximately 18 minutes and the median time is 13 minutes.

If Jacob uses the median time, then he's correct because he travels for 17 minutes and that is longer than average.

However, Jacob's family could counteract this argument by saying that if they use the mean, then Jacob is actually travelling for less time than average.

So it depends on who you chose to support there.

It's time to sum up what we've learnt today.

Some calculators can perform more than just basic calculations.

The fx-991CW can produce a statistical summary of a set of data.

The summary includes the mean, median, upper and lower quartiles.

Well done.

You've worked really well today.

I look forward to seeing you for more maths in the future.

Goodbye for now.