Statistics
Measures of Dispersion
JEE Main 2022
Grade 11
Question:
Two data sets $A$ and $B$ have the same mean, but $A$ has a smaller standard deviation than $B$. Which of the following is true?
(1) $B$ is more consistent than $A$
(2) $A$ is more consistent than $B$
(3) Standard deviation gives no information about consistency
(4) The data set with the larger mean is more consistent
Step-by-Step Solution
Key Concept: Recall that the standard deviation measures how spread out the observations are about the mean — a smaller spread corresponds to greater consistency (less variability) in the data.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)