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 will be able to use the fx-83/85GT CW to perform calculations with data.

Now on the screen, you've got some keywords that we're going to be using in our lesson today.

They should be familiar to you, but if they're not, feel free to pause the video now while you have a read through.

And here is some more.

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

The first part of the lesson, we're going to look at how you find 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 Izzy wants to know, does this mean she needs to use the calculate mode to add all the numbers before dividing? And Jun says you can, but there's a much easier way to calculate the mean.

So remember, in this lesson we're using the Casio fx-83 or 85GT CW model.

We're gonna cover how to use the calculator to carry out different calculations.

So switch the calculator on, and you'll see this screen.

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

Remember, we're gonna be looking at how to calculate the mean from a frequency table.

So we need to navigate to the Statistics option and press the Execute button.

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

This represents three tables, each with four diners.

This represents two tables, each with five diners.

We're dealing with one set of data.

So we choose 1-Variable from the Statistics menu on our calculator.

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

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

Time for quick check.

Enter 0 and press Execute.

What value appears in the Frequency column? Pause the video while you have a go at this now.

Welcome back.

You should have seen that the value 1 appears.

1 is the default frequency value.

You can change the value by navigating to the value you wish to change, type in the correct value and pressing Execute.

Enter the remaining values now into your calculator.

Pause the video while you do this.

Welcome back.

The bottom half of your table should now look like this.

Remember, you can use the arrow keys to scroll up and down your table.

Once all the values have been correctly entered, you press Execute, and this screen appears.

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

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

What is the value of the mean? Pause the video and write this down now.

That's right.

The mean is 3.

"But what if I have a frequency bar chart and not a table?" Jun says, "Well, you could just read the values of the bar chart to create the table." To quickly clear all existing data in the table, you can press Tools and then select Edit and Delete All.

You now have a blank table to put the new values into.

Alternatively, you can just overwrite the existing values.

Whatever you think is easiest.

This bar chart shows reviews of a restaurant.

What will the correct first row of the table look like? Pause the video and work this out now.

Welcome back.

You should, of course, have chosen C.

Now A is what you get by default, but that's not the correct first row.

You would need to go and change the frequency.

Carry on now and calculate the mean rating for this restaurant.

Pause the video while you do this.

Welcome back.

The mean rating is 3.

35 stars.

It's now 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 while you work this out now.

For 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 while you work this out now.

Question three: A class take a quiz marked out of six.

The frequency table shows the results for the class.

What is the mean number of marks per pupil? Pause the video and work this out now.

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

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

Welcome back.

Final question now, question five: The bar chart shows the length of time customers spent waiting at a self-service till, to the nearest minute.

What is the mean wait time? Pause the video and work this out now.

Welcome back.

Let's go through our answers.

So for question one, 1.

65 goals was the mean number of goals scored, which you could, of course, have rounded to 2, because 1.

65 goals doesn't make sense in context.

You can't have 0.

65 of a goal.

So if you said 2, spot on.

Question two: The mean star rating was 3.

64, et cetera stars, which, of course, rounds to 4.

Question three: the mean number of marks per pupil was 3.

Question four, the mean number of bedrooms was 2.

5, which again, you could have rounded to 3.

And then question five, the mean wait time was three minutes.

Well done if you got those all right.

Did you find it easier to use your calculator to calculate the mean, rather than trying to do it all yourself? Hopefully you did.

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

We're gonna be doing some analysis.

Let's see what we mean.

Now, our calculator can do more than just calculate the mean.

Izzy points out that when she 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 go back to this example: A table showing the number of diners at various tables in a restaurant.

When we calculated the mean, we saw all this information displayed.

Pressing the down arrow key reveals even more information.

In fact, there are two more pages worth.

We're gonna consider the information needed for GCSE Maths.

So there's quite a lot here, but we don't need all of it for the GCSE.

So we're just gonna focus for now on these bits.

And if you go on to study maths after your GCSE, then you're gonna find it very useful that your calculator can work out even more for you.

The mean is represented here at the top of the screen.

This is the sum of the values.

Now, it could also be written as the sum of f multiplied by x.

On the second screen, we've got n being the number of values.

So there are 11 distinct values here.

Min(x) means the minimum x value.

Q1 refers to the lower quartile, Med refers to the median, and Q3 refers to the upper quartile.

Max(x) refers to the maximum x value.

Let's do a quick check.

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

Remember, the interquartile range is found by taking the upper quartile and then subtracting the lower quartile.

Pause while you work this all out now.

Welcome back.

For the mean, we should have 3.

For the median, we should have 3.

And the inter quarter range is 4 - 2, which gives us 2.

Well done if you've got these all right.

It's now time for our final task.

So for 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.

For part A, calculate the median.

Part B, calculate the interquartile range.

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

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

A developer wishes to build more expensive houses, so that means three or more bedrooms. But the local council want cheaper housing.

The council argue 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 while you work this out now.

Question four: The bar chart shows the length of time customers spent waiting at a self-service till to the nearest minute.

Management want every customer to be queuing for less than the average queue time.

Part A, calculate the average queue time, and in part B, explain why it's not possible for everyone to queue for less time than the average queue time.

Pause the video and work this out now.

Welcome back.

Time to go through our answers.

For question one, the median is 1 goal.

And part B, the interquartile range is 2 goals.

Part C, what would the club prefer to report? Well, the club would prefer to report the mean as it rounds to 2 goals, which looks a lot better than the median of only 1 goal.

So it makes the club's performance look better.

Well done if you said that or something similar.

Question two: The median is 4 stars and the interquartile range is 2 stars.

Part C: What would the restaurant prefer to report? Well, actually, they could report either, but the median didn't require any rounding.

So maybe you said something like that.

Well done if you did.

Question three: Are the council correct? Well, if we calculate the mean, that's 2.

5 bedrooms and the median is 2.

The interquartile range was 1.

So this is an example of what you could have put.

If the council uses the mean, then they can round and state that the average number of bedrooms in houses in this area is 3.

Therefore, there are plenty of houses with 3 or more bedrooms in.

So that's a way to support their argument that we've got enough expensive housing, we need cheaper housing.

Question four: Calculate the average queue time.

Well, actually the mean and the median and the mode are all 3 minutes.

Part B: Why is it not possible for everyone to queue for less time than the average queue time? Averages are a measure of central tendency.

It is possible for everyone to queue for the average time, but not for everyone to be below if everyone's time decreased so would the average.

Well done if you did something like that.

Maybe you used numbers to justify your answer.

Well done.

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

Some calculators can perform more than just basic calculations.

The fx-83 or 85GT CW can produce a statistical summary for a set of data.

The summary includes the mean, median, upper and lower quartiles, along with a lot of other information.

Well done, you've done really well today and I look forward to seeing you for more maths in the future.

Goodbye for now.