ExamBro
ExamBro
TS EAMCET · Maths · Statistics

The standard deviations of two sets of observations \(X=\left\{x_i\right\}\) and \(Y=\left\{y_i\right\}\) \((i=1,2, \ldots, 100)\) are respectively 5 and 6 . If \(\bar{x}, \bar{y}\) are their means and \(\sum_{i=1}^{100}\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)=600\), then the standard deviation of \(Z=\left\{z_i / z_i=x_i-y_i\right)\) is

  1. A 12
  2. B 6
  3. C 7
  4. D 10
Verified Solution

Answer & Solution

Correct Answer

(C) 7

Step-by-step Solution

Detailed explanation

From the given information, we can say that \(\sqrt{\frac{\sum_{i=1}^{100}\left(x_i-\bar{x}\right)^2}{100}}=5 \text { and } \sqrt{\frac{\sum_{i=1}^{100}\left(y_i-\bar{y}\right)^2}{100}}=6\) \(\therefore \quad \sum_{i=1}^{100}\left(x_i-\bar{x}\right)^2=2500\) and…