umm ok this is a method known as assumed mean, you basically take a number and assume that it is the mean of a set of numbers (lets say we have 16, 17, 19, 21, 22) so I 'assume' the mean is 20 and the i calculate the difference of every number from that assumed mean. first lets just do it. then i'll explain this in statistical sense
so the five numbers are
16, 17, 19, 21, 22 and the assumed mean was 20, so find the difference for each of these numbers from 20,= -4, -3 ,-1, 1, 2 these are the respective differences
so you add all the differences and you have -5
so you have the sum of (x - 20) = -5
since there were five numbers, divide -5 by 5
x-20 = -5/5
x-20 = -1
x = 19 (voila, this is the real mean)
so when in your question they give you
Σ(x-45) = -148 45 here is the assumed mean, and -148 is the added difference of 36 values from 45
x-45 = -148/36
x-45 = -4.11
x = -4.11 + 45
x = 40.89 (the real mean)
= 40.9 (to one d.p.)
so the formula for the mean is
[ Σ(x-a) ]/ n , a is the assumed mean and n is the number,
similarly in the question there is given Σ(x-45)^2 = 3089 (i'll use Σ(x-a) as Σy so Σ(x-a)^2 will be Σy^2
the variance is calculated by [(Σy^2 )/n ] - [y' ^2] (y' is the mean)
sorry that looks so complicated umm in words variance is Σ y^2 divided by n, minus the mean squared
and standard deviation will be squareroot of variance
Oh thank you so much !! but one more question please . which mean is used then for the standard deviation calculation ?
