Hello and welcome to Mr Tompkins Ed Tech.
Today we are starting a new video series looking at the Casio FX-570EX or FX-991EX, and more
commonly known as the Casio Classwiz. We will be using this to find mean and standard deviation
from a Grouped frequency table containing continuous data.
So if you own this calculator, or are thinking of getting one, why not “subscribe” and
click the bell to be notified about new uploads showing you how to get the most out of the
Classwiz. In this video we’ll be generating basic
statistics for a set of data, including mean, median, quartiles, standard deviation and
variance, and how we can use this functionality to answer typical A Level statistics S1 or
IB math exam questions, just like this one. The question is based on a grouped frequency
table containing the guesses of a 40 people on the length of a road. We need to find the
mean and standard deviation of these guesses, which is no problem at all for the classwiz.
The calculator has a function that will happily generate these statistics and a whole lot
more besides with just a few key presses. So lets pull up the Classwiz. I’m using
an emulated version here so that I can capture the outputs more easily, but it works just
the same as the real thing. Just a little bit less shiny.
To get into stats mode, press the “Menu” button, followed by “6”. We are given
a range of choices here, and we want the first choice – “1-Varable”, so press “1”.
Now the default here is one column, allowing you to enter a list of numbers. We don’t
want to type in all 40 numbers individually, so we need to tell the calculator to add a
second column for frequency. We can do this by pressing “SHIFT” followed by “SETUP”,
the down arrow, and “3” for statistics. Press “1” to turn frequency on, and you
can see we now have the right setup for a frequency table.
The first column is for our L values but our table has ranges for these and the calculator
only wants one number. So we are going to use the mid-values as estimates for each, which
we can find by averaging the upper and lower class boundaries of each group. When calculating
these, it is important to first consider whether the data is discrete or continuous and how
the values were rounded up or down. Now the values of L represent distance, which is a
continuous quantity and we are told it has been rounded to the nearest km. So the first
group 10-12 actually represents all values of L between 9.5 and 12.5 km. So the average
of these is 9.5 + 12.5 divided by 2, which gives us 11. Now notice in this case we get
the same result as if we had just used 10 and 12, but this is not always the case and
you will need to consider boundaries carefully whenever dealing with grouped data.
OK, applying the same thinking to our other groups we get estimated values of L of 11,
14, 18, and 25.5, which we can now type into the Calculator, along with the frequencies
1, 13, 20 and 6. So the hard work done, all we need to do now
is ask the calculator to show us the stats.
With the Classwiz we do this by press “OPTN” and then “3” for “1-Variable Calc”.
It happily churns out lots of values for us, scrolling down we can see min, median, quartiles
and max values, which will be very handy for other questions, but for this one we need
these values at the top of the list. X bar is the mean, so that's the value I'm
going to write down over here. 17.65. Then we've got all the various totals down here,
including the values for standard deviation. It would be nice if I could just write it
down and collect all the marks, but this is A level and we need to show a bit of method.
The first value I'm going to write down is sigma f, the sum of the frequencies. Now on
the classwiz that's given by n, the number of elements. So sigma f is 40.
Now sigma fx is given by the one below, sigma x, equal to 706. I’ll also need Sigma fx
squared, which is the next one down, 13050.5. I want to show enough method to make sure
I get all the available marks, so I'm going to sub these 3 values into the standard deviation
formula. So 13050.5 divided by sigma f, which is 40, minus the square of the mean, 17.06
squared. No need to type this into my calculator because
it's already been done for me. The next two values in the list are Variance and Standard
deviation, so can just write down this one as my answer. 3.84 to 3 significant figures.
Now our values for mean and standard deviation are only going to be estimates as we have
used the mid values rather than the actual guesses to calculate with, so lets write that
down in a sentence. Lets take a quick look at the markscheme.
We get a B1, or independent of method mark for the correct midvalues, a method mark and
an accuracy mark for finding the mean, an implied method mark for the total, a method
mark for the substitution and an accuracy mark our answer rounded to an appropriate
degree of accuracy. A final B1 mark for realising that the use of mid values means these are
estimates only. Don’t forget to click like or comment below
if you found the video useful and if there is sufficient interest, I’ll create more
for you, so why not subscribe? Thank you for watching and see you next time
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