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Q 109. If a Standard deviation of x is o, then Standard deviation of ax + b, where a, b and c (c≠ 0) are arbitrary constants, will be
a. σ
b. ασ + b C
a C
d. σ?
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Q 109. If a Standard deviation of x is o, then Standard deviation of a...
Standard Deviation of ax + b
Standard deviation is a measure of the amount of variation or dispersion of a set of values. In this case, we are given that the standard deviation of x is σ. We need to find the standard deviation of ax + b, where a and b are constants.

Formula for Standard Deviation of a Linear Transformation
When we have a linear transformation of a random variable, the standard deviation changes according to the following formula:
- If Y = aX + b, then the standard deviation of Y is equal to |a| times the standard deviation of X.

Applying the Formula
In this case, we have Y = ax + b. Applying the formula, we get:
- The standard deviation of Y is |a| times the standard deviation of X.
- Therefore, the standard deviation of ax + b is |a|σ.

Final Answer
So, the standard deviation of ax + b, where a, b, and c (c≠ 0) are arbitrary constants, will be:
- |a|σ
Therefore, the correct answer is option (b) ασ. The standard deviation of the transformed random variable ax + b is equal to the absolute value of a times the standard deviation of the original random variable x.
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Q 109. If a Standard deviation of x is o, then Standard deviation of ax + b, where a, b and c (c≠ 0) are arbitrary constants, will bea. σb. ασ + b Ca Cd. σ?
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Q 109. If a Standard deviation of x is o, then Standard deviation of ax + b, where a, b and c (c≠ 0) are arbitrary constants, will bea. σb. ασ + b Ca Cd. σ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q 109. If a Standard deviation of x is o, then Standard deviation of ax + b, where a, b and c (c≠ 0) are arbitrary constants, will bea. σb. ασ + b Ca Cd. σ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q 109. If a Standard deviation of x is o, then Standard deviation of ax + b, where a, b and c (c≠ 0) are arbitrary constants, will bea. σb. ασ + b Ca Cd. σ?.
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