Chapter 4, Problem 15P

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10th Edition

Frederick J Gravetter + 1 other

ISBN: 9781305504912

Textbook Problem

a. After 6 points have been added to every score in

a sample the mean is found to be M = 10 and the standard deviation is s = 13. What were the values for the mean and standard deviation for the original sample?

b. After every score in a sample is multiplied by 3, the mean is found to be M = 48 and the standard deviation is .f = l 8 what were the values for

the mean and standard deviation for the original

sample?

To determine

To find mean and variance of the sample given with us.

Explanation

Here we have to find the first mean then variance and followed by SD. So, in the calculation part will see how each step has done.

**Given:**

We have given a population with mean 70 and standard deviation 13

**Formula Used:**

We know the properties of mean and Variance

Define,

Y=X+b

Z=a*X

To find the mean and Variance of Y and Z

Where X having mean m and Variance s^{2}

E(Y) =E (X +b) =E(X) +b=m+b; var(Y) =Var(X) = s^{2}

E(z)=a*E(X)=a*m; Var(Z)=var(X)*a^{2}= s^{2}*a^{2}

Here a and b are arbitrary constant

**Calculations:**

a) We need to find the mean and Variance if we added 6 with each sample point...

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