Hello and welcome to Mr Tompkins Ed Tech. This is a follow up to my “Standard Deviation
with a Casio Graphical Calculator” video. I was asked by subscribers RAFA BEAUS IRANZO
and BEN IRWIN if I could explain how we can use the calculator to find Standard Deviation
from a Grouped Frequency table containing Continuous Data. Thank you for the suggestion,
RAFA and BEN, I am very happy to oblige! If you also have a question or suggestion
for a future video, please do let me know in the comments below, and I’ll see what
I can do. If you subscribe and hit the notification bell, you’ll be notified of future uploads.
In this video i'll be showing you how to use a Casio Graphical Calculator to generate basic
statistics for data presented in a grouped frequency table, including mean, median, quartiles,
standard deviation and variance. Here is a typical A Level statistics S1 or
IB math exam questions, taken from a past paper. It 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 this Calculator.
There is 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 Calculator.
From the main Menu, press “2” for STATS mode. Lets clear out any pre-existing data
by pressing “F6”, then “F4” for DELETE ALL, and F1 to confirm for each of the columns
containing data. Done
The first column is for our L values but we have a problem here that our table has ranges
for these and the calculator only wants one number. We are going to use the mid-value
as an estimate 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
will not always be the case and you will need to consider boundaries carefully whenever
dealing with grouped data. OK, applying the same logic 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.
Press “Calc”, and then press “F6” to make sure the calculator is SET right for
a frequency table. 1-Var frequency needs to be set to “LIST2” so that the calculator
uses these values rather than assume we only have 1 of each value. That done, we can “EXIT”
, and press “F1” for 1-variable calculations. The calculator will now happily churns out
lots of values for us, scrolling down we can see min, median, mode, 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 graphical calculator that's given by n, the number of elements. So sigma f is 40.
Now sigma fx is given by the value 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 those marks for this question, so I'm just going to sub the 3 values I've written
down into the standard deviation formula. So 13050.5 divided by sigma f, which is 40,
minus the square of the mean, 17.65 squared. No need to type this into my calculator because
it's already been done for me. The next value in the list is 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. Taking 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
So RAFA and BEN, I hope you found this video useful.
Please keep the requests coming, subscribe, and check back regularly for new videos.
Thanks for watching and see you next time
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