Hello and welcome to Mr Tompkins Ed Tech.

In this video we will be taking another look at the Casio Graphical Calculator and how

we can use it to solve exam style problems taken from real A level S1 Statistics and

probability papers. Those of you following an IB Higher Level Mathematics or IB Biology

course will also find the style of question spookily familiar, so keep watching. In the last video we looked at the single

variable calculation function, and used it to find mean and standard deviation. This time we will be looking at how the Casio

Graphical Calculator copes with two variable, or bivariate data. We will be using the graphing

tool to plot a scatter graph, and the 2 variable CALC function to generate a value for the

Pearson’s Product Moment Correlation Coefficient, or PMCC. So here is the exam question. It concerns

itself with a city council’s attempt to reduce traffic congestion by charging motorists to

enter the city centre. The council started with a charge of £4 in the first year, and

increased it by £2 in each subsequent year. It is always important to read the question

carefully as the context can give strong clues as to the expected answer. In this case, we

would expect to find that as the council increased the charge, the number of vehicles entering

the city would fall. This would imply a strongly negative value for PMCC, and so if our calculation

doesn’t show us this, it should alert us that we may have made a mistake somewhere along

the line and we should probably go back and check it. It’s much better to find out you

have made a mistake whilst you are in the exam hall and can still do something about

it, rather than when the results come in. Ok, so lets start entering the data into the

calculator and see what it gives us. So first up, put the calculator in STATS mode, which

is 2 on the main screen. That brings up this screen, which has multiple

columns to enter lists of data. This time because we have bivariate data, we need two

lists to hold our values from the data table. Before we put the new data in, lets clear

out anything that is already in the memory from the last time we used it. First we press

F6 to bring up the 2nd menu of functions, followed by F4, which is the Delete All function,

and F1 to confirm. This will clear out all the values in the currently selected list.

Now, move the cursor into the second column and then press F4 followed by F1 again to

get rid of List 2. Right having now tidied up, we can start entering

our new data. We will use LIST 1 to hold the Charge, in

£s, and LIST 2 to hold the average number of vehicles per day. So 4, 6, 8, 10, 12, 14, 16, 18, then tap the

right arrow for list 2, and we enter 2.4, 2.5, 2.2, 2.3, 2.0, 1.8, 1.7, 1.5. Done. Right, so F6 brings us back to the original

menu of functions and we want to tap F1 to graph the data. The calculator lets you store up to 3 presets

for graphs, and you can press the SET button to define what you want these to be. At the

moment I have graph 1 set up to draw a box plot and graph 2 to draw a scatter graph and

graph 3 to draw a pie chart, but you can set these to whatever you want from the 20 or

so available graph types the calculator can draw. Now for a scatter graph, you need to tell

the calculator where to pull its x and y values from. So we are using list 1 and list 2 for

these. The frequency should be 1, and you can choose what sort of mark type you want

to show. Once you have this set up, press EXIT, and

select the preset you used. I used Graph 2, so I’ll press F2. Unsurprisingly we have a scatter graph showing

strong negative correlation. This fits with the context, as we suspected that as the charge

went up it would drive the number of vehicles down. Sadly we cant just print this out and stick

it on our exam paper, but we can use it as a visual check that our hand-drawn graph is

correct. Once the graph is drawn, you can use the trace function SHIFT F1 to show the

actual plot points and their values and use this to double-check the values on your drawn graph. So having drawn your graph and checked it

with your calculator, we are ready for the main event – calculating PMCC. Now PMCC is always a number between 1 and

-1, with numbers close to 1 showing strong positive correlation and close to -1 showing

strong negative correlation. We have already noted that our scatter graph clearly shows

strong negative correlation, so we are expecting an answer around negative 0.9 here. Right lets hit the F2 CALC button, and quickly

check SET to make sure we are configured correctly for bivariate data. Check that the 2VAR XList

points to List 1, and that the 2Var YList points at List 2. If it doesn’t for some reason,

you can press the LIST button and set it correctly. Now press EXIT, followed by F2 2VAR and see

what numbers we get. You can see it generates the totals, mean

and standard deviation, along with the min and max values for both the x and the y datasets. We can use this screen to copy down the totals

if they are not given in the question itself. For the PMCC calculation, we will need n,

the number of elements, Sigma X, Sigma Y, Sigma X squared, Sigma Y squared, and Sigma

XY. Lets write all those down. n is 8, sigma x is 88, sigma x squared is

1136, scrolling down, Sigma y is 16.4, sigma y squared is 34.52 and sigma xy is 168.6 Whilst your calculator will also churn out

a value for PMCC, you will need to show method to get all the marks. So lets write down the

PMCC formulae. We would normally need to evaluate these 3

formula and then sub our answers into the 4th to find PMCC, but as we are smart and

we are going to use the calculator to take the sting out of this a little, to minimise

our effort and so allow us more time for other more challenging parts of the exam paper. We are going to do all 4 at once. This way,

we don’t actually need to evaluate each section separately, thus minimising the risk of making

a calculation error, and can just write down the final answer. So here goes. It’s a bit of a beast, but with

a little care it’s not too bad. Now, there is no need to actually type this

behemoth into the calculator. We just need to go to EXIT and choose F3 for the regression

function. We will cover the regression function in much more detail in the next video. For

now we will just select F1 for X, or linear regression. Now both the y-on-x or x-on-y

regression functions will give us the same value of PMCC, so it doesn’t matter which

one I choose. So lets go for ax+b. PMCC is given by this r value, so I just need

to copy that down to an appropriate degree of accuracy. So minus 0.960 to 3 significant

figures. Done. Easy peasy, and our answer is reassuringly close to -1, as we expected

it to be. Now the mark scheme states 2 method marks

and 1 accuracy mark for this question. You get the first method mark for a correct substitution

into any S formula, and the second for a correct substitution into the r formula. We have done

both at the same time. We will get the third and final accuracy mark by writing down the

correct value for PMCC. Now there is no getting around the fact that

you need to learn these formula, and you will also need to be able to substitute carefully

into them to gain the method marks. However, the graphical calculator has done the hard

number crunching, so you don’t have to, saving you time and minimising the risk of making

a typing error in this otherwise long and intricate calculation. So that’s all for this video. You should now

know how to use your Casio graphical calculator to plot a scatter graph and to find PMCC the

easy way. Please like if you found it useful, and leave

a comment if you have any questions or suggestions. In the next video in this series, I’ll be

delving into the linear regression function in much more detail. I’ll be showing you how

to find y-on-x and x-on-y regression lines, along with some explanation on when you should

use one or the other. So please hit subscribe so you will be notified of this and any future

uploads. Thanks for watching and hope see you next

time. ## More videos on Statistics available from

MrTompkinsEdTech Channel ##

## 8 Comments

Legend.

thank you !!!

Thank you so much

can you let me know how I put my fx-9750GII calculator in exam mode? I have my s1 exam tomorrow and I don't know how to enter exam mode, will the invigilators come and do it for me?

Hi Mr I am in your class

Please give some tutorial using this calculator

I learned more in this video than in my entire school term. Thanks!!!

Hi Mr T

Thank you for your very useful videos. What I want to do is use results from my graphs when doing calculations in run-matrix mode. How can I copy values between modes please?