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If the standard deviation of a data set is 0, what can be said about the data?

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Question: If the standard deviation of a data set is 0, what can be said about the data?

Options:

  1. All values are different
  2. All values are the same
  3. Values are in a range
  4. Data is not valid

Correct Answer: All values are the same

Solution: 

A standard deviation of 0 indicates that all values in the data set are the same.

If the standard deviation of a data set is 0, what can be said about the data?

Practice Questions

Q1
If the standard deviation of a data set is 0, what can be said about the data?
  1. All values are different
  2. All values are the same
  3. Values are in a range
  4. Data is not valid

Questions & Step-by-Step Solutions

If the standard deviation of a data set is 0, what can be said about the data?
  • Step 1: Understand what standard deviation means. It measures how much the values in a data set vary or spread out from the average (mean).
  • Step 2: Recognize that a standard deviation of 0 means there is no variation in the data.
  • Step 3: Conclude that if there is no variation, all the values in the data set must be identical.
  • Step 4: Therefore, if the standard deviation is 0, it means every number in the data set is the same.
  • Standard Deviation – A measure of the amount of variation or dispersion in a set of values.
  • Data Uniformity – When all values in a data set are identical, the standard deviation is zero.
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