Question
Download Solution PDFThe arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Given,
Number of observations, n = 100
Original arithmetic mean, \( \bar{x} = 50 \)
Transformation applied to each observation:
New value, \( x' = \frac{x - 5}{20} \)
The new arithmetic mean is,
\( \bar{x}' = \frac{\bar{x} - 5}{20} \)
\( \bar{x}' = \frac{50 - 5}{20} = \frac{45}{20} = 2.25 \)
∴ The new arithmetic mean is 2.25.
Hence, the correct answer is Option 1.
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