defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Statistics Variance and Standard Deviation
Let \(\overline x\), M and \(\sigma^2\) be respectively the mean, mode, and variance of n observations \(x_1, x_2, \ldots, x_n\) and \(d_i = -x_i - a, i=1, 2, \ldots, n\), where a is any number.
Statement I: Variance of \(d_1, d_2, \ldots, d_n\) is \(\sigma^2\)
Statement II: Mean and mode of \(d_1, d_2, \ldots, d_n\) are \(-\overline x - a\) and \(-M - a\), respectively
1
Statement I and Statement II are both false
2
Statement I and Statement II are both true
3
Statement I is true and Statement II is false
4
Statement I is false and Statement II is true