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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Statistics

NDA 2019 · Mathematics · Statistics

The mean of 100 observations is 50 and the standard deviation is...

The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4 , then what will be the new mean and the new standard deviation respectively?

Options

  1. A45,5
  2. B11.25,1.25
  3. C11.25,2.5
  4. D12.5,2.5

Correct answer

C. 11.25,2.5

Step-by-step solution

Number of observations (N)=100(\mathrm{N})=100 Mean (xˉ)=50(\bar{x})=50 Standard deviation (σ)=10(\sigma)=10 New mean, \bar{x}_{\mathrm{I}}=\frac{\Sigma \frac{x-5}{4}}{N}=\frac{1}{4}\left(\frac{\Sigma x}{N}-5\right)=\frac{1}{4}(50-5)=\frac{45}{4}=11.25 New standard deviation (σ1)=σ(x−54)=14σ(x−5)=14σ(x)=104=2.5\left(\sigma_1\right)=\sigma\left(\frac{x-5}{4}\right)=\frac{1}{4} \sigma(x-5)=\frac{1}{4} \sigma(x)=\frac{10}{4}=2.5
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