Anyone got any suggestions for this maths problem? Been trying for ages and i cant work it out!?

Question

The mean of the real numbers q, r, s, and t is x. and the standard deviation is d.

Consider the numbers aq+b, ar+b, as+b, and at+b, where a and b are real and b is greter than 0.

Show that the mean of these numbers is ax+b.
Show that the standard deviation is ad.

Answer 1

make the sum

aq+b +ar+b+as+b+at+b = a(q+r+s+t)+4b=S

the mean is the sum divided by 4
S/4 = a(q+r+s+t) +4b/4 =( a(q+r+s+t) )/4 +b = ax+b

Standard deviation . when you and a constant to each term of a population you do not change the standard deviation

So compare toqrst , you have only multiplied all terms by a, and the standard deviation is multiplied by a

Answer 2

The mean is

((aq + b) + (ar + b) + (as + b) + (at + b))/4
or
(a(q + r + s + t) + 4b) / 4
or
since (q + r + s + t)/4 = x
then
ax + b

I am sure if you work the math for standard deviation you will get the desired result also.

Answer 3

you have to set the first set of number equal to the average and then do the same for the second set of equations and factor out the original set in order to reveal the ax+b solution.

good luck