Question

The mean test score was 70 points, and the standard deviation was 15 points. If I add 10 points to everyone's test score, what is:

a) the mean test score for the class after the 10 points is added to each score?

b) the standard deviation of the test scores for the class after the 10 points is added to each score?

Answer 1

Suppose we start with a random variable X , and transform it

Y = a*X + b

mean of Y = a * (mean of X) + b

so here you want to add 10 points to each score, this means
we have a new random variable

Y = X + 10

mean of Y = mean of X + 10

Answer 2

X represents the old data values

Y represents the new data values after you do some kind of transformation (multiply each data point by some number, or add some number to each data point)

Answer 3

From earlier explanation, I concluded the new mean would be 80. Does that sound right?

Wouldn't the Standard Deviation stay the same?

Answer 4

yes, the new mean is 80 and the st. dev stays the same

Answer 5

In general , let SD = standard deviation, and M = mean

SD ( a*X + b) = a * SD(X)

M ( a*X + b) = a* M(X) + b

Answer 6

and here we have a = 1 , b = 10

SD ( 1*X + 10 ) = 1 * SD( X)

M ( 1*X + 10) + 1* M(X) + 10

Answer 7

Ok, you lost me with all the variables and formulas, he didn't teach us those. Thank you!