A student calculated mean and standard deviation of observations as and respectively. Later it was discovered that he had taken by mistake instead of , then new standard deviation is:

5 Explanation: Given Data: Number of observations ( ) = Incorrect Mean ( ) = Incorrect Standard Deviation ( ) = Incorrect value read = Correct value to be replaced = Step 1: Find the Correct Mean First, find the incorrect sum of observations ( ): Now, calculate the correct sum of observations ( ) by subtracting the incorrect value and adding the correct value: Therefore, the correct mean ( ) is: Step 2: Find the Correct Sum of Squares ( ) The formula for variance ( ) is: Using the incorrect data values: Now, find the correct sum of squares ( ): Step 3: Calculate the New (Correct) Standard Deviation Substitute the corrected values into the variance formula: Taking the square root on both sides gives the new standard deviation: Conclusion The new standard deviation is . Correct Option: (a)

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NIMCET 2007 — Mathematics PYQ

NIMCET | Mathematics | 2007

A student calculated mean and standard deviation of $100$ observations as $40$ and $5.1$ respectively. Later it was discovered that he had taken by mistake $50$ instead of $40$ , then new standard deviation is:

NIMCET 2007 — Mathematics PYQ

Choose the correct answer:

Explanation

Given Data:

Step 1: Find the Correct Mean

Step 2: Find the Correct Sum of Squares ( $\sum x_{correct}^{2}$ )

Step 3: Calculate the New (Correct) Standard Deviation

Conclusion