A population has a mean of 30 and a standard deviation of

A population has a mean of = 30 and a standard deviation of = 5.

(a) If 5 points were added to every score in the population, what would be the new values for the mean and standard deviation?

Mean:

Standard Deviation:

(b) If every score in the population were multiplied by 3, what would be the new values for the mean and standard deviation?

Mean:
Standard Deviation:

Solution

A)

Note that

u(x+c) = u(x) + c
s(x+c) = s(x)

Thus, the mean will increase by 5, but the standard deviation will not change.

Hence,

new mean: 30 + 5 = 35
new standard deviation: 5 [answer]

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b)

Note that

u(cx) = c u(x)
s(cx) = x s(x)

Thus, both will be multiplies by 3:

new mean: 30*3 = 90
new standard deviation: 5*3 = 15 [answer]