Understanding Data Transformation Effects

The video tutorial explains how transforming data affects measures of center and spread, focusing on mean and standard deviation. It demonstrates that adding a constant shifts the mean but not the standard deviation, while multiplication affects both. Guidelines for understanding these transformations are provided, using examples to illustrate the concepts.

What is the mean weight of the sample of university students from Winnipeg?

• 750 milliliters

• 135.6 pounds

• 140.6 pounds

• 31.75 pounds

How does adding a constant value to each data point affect the mean?

• It does not change the mean.

• It doubles the mean.

• It increases the mean by the constant value.

• It decreases the mean by the constant value.

What happens to the standard deviation when a constant is added to each data point?

• It increases by the constant value.

• It doubles.

• It remains unchanged.

• It decreases by the constant value.

Which of the following operations affect measures of center?

• All mathematical operations

• Addition and subtraction only

• None of the operations

• Multiplication and division only

Which operations affect measures of spread?

• Addition and subtraction

• Multiplication and division

• Only subtraction

• Only addition

In the water consumption example, what is the multiplicative factor used?

• 2.5 milliliters

• 5 pounds

• 750 milliliters

• 135.6 pounds

How is the new mean calculated in the water consumption example?

• By multiplying the original mean by 2.5 and adding 750

• By dividing the original mean by 2.5

• By adding 750 to the original mean

• By subtracting 750 from the original mean

What is the new standard deviation in the water consumption example?

• 79.38

• 31.75

• 1089

• 135.6

What formula represents the transformation of measures of center?

• New center = Old center / Multiplicative constant

• New center = Old center * Multiplicative constant

• New center = Old center * Multiplicative constant + Addition constant

• New center = Old center + Addition constant

How is the new spread calculated according to the transformation formula?

• New spread = Old spread - Addition constant

• New spread = Old spread / Multiplicative constant

• New spread = Old spread * Multiplicative constant

• New spread = Old spread + Addition constant