Question

Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 25, what are the new mean and standard deviation?

Answer 1

New man would be 525 but the standard deviation will remain same.

Step-by-step explanation:

The average score on a national test is 500 with a standard deviation of 100.

Now each score is increased by 25.

Let y = x + 25

where x represents old mean and y represents new score

Given E(x) = 500  and standard deviation (x) = 100

E(y) = E(x + 25)

      = E(x) + 25

      = 500 + 25

      = 525

Variable (y) = Variable (x + 25)

                   = Variable (x)

⇒ $\sqrt{var(y)}=\sqrt{var(x)}$

⇒ SD(y) = SD(x)

             = 100

New man would be 525 but the standard deviation will remain same.

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