Measures of dispersion – ACCA MA
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Hi Sir,
I am parallelly studying ACCA notes with your lectures. I found two equations to calculate variance.
1. The formula for calculating the variance of ungrouped data = ?(x ? x?)2 /n
2. The formula for calculating the variance of grouped data = ?f(x ? x?)2 /?f
Why are you using only the grouped data equation for both? Can you explain me how to choose the right equation? I understand usage of group equation in example 3.
Hello sir, in first illustration 1.46 squared must equal to 2.1316
Dear John,
The Formula sheet provides 2 Formulas to Calculate Standard Deviation;
You have Used the 1st one in this lecture: ?= ??(????)2 ÷ n
Can we use the 2nd one: ?= ?(? ??² ÷ ? ?) ? (? ?? ÷ ? ?)²
in arriving at the same answer at the Examination?
You can use either formula – they give the same answer – but I find the first one the easier and quickest.
Thank you for the lecture
Is there a specific reason why you dont use the formula given in the exam to work out standard deviation?
I have a small doubt sir. If I do the total of all the f(X-X bar) in example 5, why is it not coming out to be 0 as it should ?
It is because we had rounded the average to the nearest $ rather than having used the exact figure 🙂
Thank you so much Prof.
I did the calculation and the Sigma (x-x)^2 is 17514428
True – I must re-record the lecture. However the printed answer in the lecture notes is correct ?
Thanks.
Hello Sir
First of all, thank you so much for the wonderful lessons
You explain very nicely why when we want to know what is the VARIANCE we need to make the numbers SQUARED because if you did not turn them then the plus would balance with the minus and we would reach zero
My question is this: after all, the numbers are supposed to be equal on both sides of the arithmetic mean, so why can we not just take only one side of the ARITHMETIC MEAN and divide it by only half the amount and then we were supposed to get a fair result???
post Scriptum. I tried it on my calculator and came up with a different result
What you suggest would be a measure of spread (and will give a different result) but is not one that we ever use, because there is no further use for it.
The variance and from it the standard deviation are useful in normal distribution theory as is explained in my lectures on the normal distribution.
Hi John, how do we know when to use the formula for population variance and when to use the formula for sample variance? I.e. when do we know to divide just by n or by n-1 when calculating variance? TIA!
Sampling theory (which Is what this question seems to be referring to) is not in the syllabus for Paper MA. It used to be a long time ago, but that is many years ago now 🙂
SORRY TO SAY BUT I GUESS U GOT THE ANSWER OF SIGMA X-X2 WRONG IT IS 17514428 NOT 17694428
True – I must re-record the lecture. However the printed answer in the lecture notes is correct 🙂
Thanks.
(Please don’t type in capitals 🙂 )
Excuse me sir, I cant find practice questions of this chapter.
There are none. However there will be lots of questions in your Revision Kit (and it is absolutely essential that you have a Revision Kit from one of the ACCA approved publishers because they are full of exam standard questions for practice).
Sorry to ask but how is Arithmetic Mean $1817 worked out?
I show the calculation in the previous lecture working through example 2 in this chapter !!!