The standard deviation of a data set is 5. If all values are increased by 2, wha

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Question: The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)

Options:

Correct Answer: 5

Exam Year: 2020

Solution:

Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.

The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)

The standard deviation of a data set is 5. If all values are increased by 2, what will be the new standard deviation? (2020)

Step 1: Understand what standard deviation means. It measures how spread out the numbers in a data set are.
Step 2: Know that when you add a constant (like 2) to every number in the data set, it shifts all the numbers up but does not change how spread out they are.
Step 3: Since the spread of the data (the standard deviation) is not affected by adding a constant, the new standard deviation remains the same.
Step 4: Therefore, if the original standard deviation is 5, the new standard deviation after adding 2 to all values is still 5.

Standard Deviation – A measure of the amount of variation or dispersion in a set of values.
Effect of Constant Addition – Adding a constant to all values in a data set does not change the standard deviation.