Question

In a class consisting 5 students, the original scores (X) for the 5 students on a certain exam are: 25,36,49,64,81. The instructor decides to curve the original scores, and the following two formulas are considered:

Y = 0.5X + 50

Z = 10(√ X)

(a) Find µX, σX, the mean and standard deviation of the original scores. (For σX, you may round to the nearest integer if necessary.)

(b) Find µY , σY , without computing the values of Y ’s.

(c) Can you compute µZ, σZ, without computing the values of Z’s? Why or why not?

(d) Compute µZ, σZ.

Answer 1

(a) Here n = 5 (Number of observations)

= (25+36+49+64+81)/5 = 255/5 = 51

= /5

=

= 394.8

(b) Y = 0.5X+50

Hence,

=>   (Expanding)

(SInce is constant, summing its square n times is equevalent to multiplying it's square by n)

Since

(Expanding

= 197.4

(c) Here

However since its a non linear finction of X, its impossible to calculate values of by

So its impossible to calculate mean and sd of Z by X (rather not computing values of Z)

(d) Here Z = = 50,60,70,80, 90

Hence

And

(Answer)