Suppose that every element in a sample data set is multiplie

Suppose that every element in a sample data set is multiplied by -3. For example, if the data {-3, 4, 1}, the new data set would be {9, -12, -3}. Under this transformation of multiplying every by -3, what would happen to the sample standard deviation? 21. Consider the following three statements: Which of these statements are true?

Solution

1. b) It would increase by a factor of 3. Let X be a random variable. Let Y = a * X. Then standard deviation of Y = a * Standard deviation of X.

2. b) Only (ii) and (iii) are true. This is because: categorical variables are inherently discrete. For example, a bulb can either fail or not fail, a car can be either red or blue etc.

3. (c) is the correct answer.