Question:
If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained:
If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained:
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Adding or subtracting a constant to all observations does not affect the variance; it only shifts the data.
Updated On: May 15, 2025
- increases by \( k \)
- do not change
- is equal to \( k^2 \)
- is equal to \( 2k \)
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The Correct Option is B
Solution and Explanation
The variance is not affected by the addition or subtraction of a constant value \( k \). It only depends on the spread of the data points. Therefore, the variance remains unchanged.
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