Question

24. Pick 5 numbers and compute the population standard deviationof the numbers

a. Add a nonzero constant c to each of your original numbers, and compute the standard deviation of this new population.

b. Use the results of part a and inductive reasoning to state what happens to the standard deviation of a population when a nonzero constant c is added to each data item.

25. Pick 6 numbers and compute the population standard deviation of the numbers

a. Double each of your original numbers and compute the standard deviation of this new population

b. Use the results of part a and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.

Answer 1

Answer with given data and tables are given below:

b)

From the above it is clear that standard deviation of original data is same as standard deviation of new data.

That, is adding a non-zero constant does not affect standard deviation.

Therefore, SD(X+C)=SD(X).