JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q87

← JEE Main 2014 · 19 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 87 of 90

Let $\bar x$ , M and $\sigma^2$ be respectively the mean, mode and variance of n observations $x_1,x_2,\dots,x_n$ and $d_i=-x_i-a$ , $i=1,2,\dots,n$ , where a is any number.

Statement I : Variance of $d_1,d_2,\dots,d_n$ is $\sigma^2$ .

Statement II : Mean and mode of $d_1,d_2,\dots,d_n$ are $-\bar x-a$ and $-M-a$ , respectively

Statement I and Statement II are both false

Statement I and Statement II are both true

Statement I is true and Statement II is false

Statement I is false and Statement II is true

Answer and worked solution

Official answer: B

$d_i=-x_i-a$ is a reflection and a shift.

Variance: unchanged by the shift, and multiplied by $(-1)^2=1$ , so still $\sigma^2$ .
Mean and mode transform the same way: $-\bar x-a$ and $-M-a$ .

Both statements are true.

Topics:Variance and standard deviation Measures of central tendency

← Previous question Next question →

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 87