What is the standard deviation of a dataset where all values are identical (e.g., 7, 7, 7, 7, 7)?
Answer and explanation
Correct answer: D. 0
for all observations.
Since the sum of squared deviations is , the variance is , and the standard deviation is .
Since the sum of squared deviations is , the variance is , and the standard deviation is .
- Step 1: The standard deviation measures the dispersion or spread of values around their arithmetic mean. For the dataset , the mean is .
- Step 2: Compute the deviations of each data point from the mean :
Answer
0.
Why not the others: The values 7, 1, and 'Undefined' confuse the mean of the data with dispersion, assume unit variance, or misidentify variance existence.
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