Bunuel wrote:

On a list of peoples ages the tabulator made an error that resulted in 20 years being added to each person’s age. Which of the following statements is true.

I. The mean of the listed ages and the mean of the actual ages are the same.

II. The standard deviation of the listed ages and the actual ages are the same.

III. The range of the listed ages and the actual ages are the same.

(A) only II

(B) I and II

(C) I and III

(D) II and III

(E) I, II, and III

In a data set of persons' ages, the tabulator erroneously added 20 years to each person's age. Effect? Which of following statements is true?

I. The mean of the listed ages and the mean of the actual ages are the same.

FALSE. The mean increases by the same constant. Listed data's age mean will be 20 years greater than actual data's age mean

Example:

Actual ages: 10 + 20 + 30 = mean of 20

\(\frac{(10+20+30)}{3} = 20)\)Listed ages: 30 + 40 + 50 = mean of 40

\(\frac{(30+40+50)}{3} = 40)\)II. The standard deviation of the listed ages and the actual ages are the same.

TRUE. Adding a constant to each value does not change the distance between values. Hence the standard deviation is the same.

Example from above

Actual: mean is 20, values 10 and 30 are SD = 10 from mean

Listed: mean is 40, values 30 and 50 are SD = 10 from mean

III. The range of the listed ages and the actual ages are the same.

TRUE. If adding a constant does not change the distance between values, then the distance between the greatest and the least value (the range), also will remain unchanged.

Example from above:

Actual: Range = (30 - 10) = 20

Listed: Range = (50 - 30) = 20

II and III are true.

Answer D

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"