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Correlation Coefficient (PMCC) on a Casio Graphical Calculator (Statistics S1/ A Level / IB)

September 15, 2019


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 ##

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8 Comments

  • Reply Mr. Verruca April 6, 2018 at 4:33 am

    Legend.

  • Reply Maëva La Palombara May 23, 2018 at 6:01 am

    thank you !!!

  • Reply Toasteh_ May 30, 2018 at 5:06 pm

    Thank you so much

  • Reply Pram x June 12, 2018 at 3:10 pm

    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?

  • Reply Nikhita Bangaru October 22, 2018 at 3:09 pm

    Hi Mr I am in your class

  • Reply AFreeThinker123 November 4, 2018 at 11:17 pm

    Please give some tutorial using this calculator

  • Reply Zachary Quinn January 9, 2019 at 2:34 pm

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

  • Reply Jenny Mathers February 24, 2019 at 10:50 pm

    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?

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