Question

If the data \(x_1, x_2, \ldots\ldots, x_{10}\) is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

• A. \(\sqrt{2}\)
• B. \(2\)
• C. \(2\sqrt{2}\)
• D. \(4\)

Hint:

Find the overall mean from the two group means, then use \(\sigma^2=\frac{\sum x_i^2}{n}-\bar x^2\).

Answer 1

The Correct Option is B

Sum of first four \(=4\times11=44\); sum of remaining six \(=6\times16=96\). Total \(=140\), so \(\bar x=\frac{140}{10}=14\).
\(\sigma^2=\frac{\sum x_i^2}{10}-\bar x^2=\frac{2000}{10}-14^2=200-196=4\).
\(\sigma=2\).
Answer: (2) \(2\)