Question
Download Solution PDFThe standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
Number of observations, n = 100
Original standard deviation, \( \sigma = 10 \)
Transformation applied to each observation:
New value, \( x' = \frac{x + 5}{20} \)
The additive constant (5) does not affect the standard deviation, and scaling by 20 divides the standard deviation by 20, so the new standard deviation is,
\( \sigma' = \frac{\sigma}{20} \)
\( \sigma' = \frac{10}{20} = 0.5 \)
∴ The new standard deviation is 0.5.
Hence, the correct answer is Option 2.
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