Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
There are $n$ observations and all of them are negative numbers. The ascending order of these observations is $x_1, x_2, \ldots ., x_n$. If the signs of the first term and last term in that order are changed, then the range of the data is
MathematicsStatisticsTS EAMCETTS EAMCET 2022 (19 Jul Shift 2)
Options:
  • A $\left|x_1\right|-\left|x_n\right|$
  • B $\left|x_{\mathrm{n}}-x_1\right|$
  • C $\left|x_1\right|-x_2$
  • D $\left|x_1\right|-\left|x_2\right|$
Solution:
1192 Upvotes Verified Answer
The correct answer is: $\left|x_1\right|-x_2$
Given, $x_1, x_2, x_3 \ldots \ldots \ldots \ldots . . . . x_n$ are negative numbers in ascending order. this can be written as $-x_1,-x_2,-x_3 \ldots \ldots \ldots \ldots .,-x_n\left\{\right.$ where $x_i>0$ and $\left.i=1,2,3 \ldots n\right\}$ now according to question $-x_1$ is replaced by $x_1$ and $-x_n$ is replaced by $x_n$ $\Rightarrow \mathrm{x}_1$ will be largest term and $x_2$ will be lowest term in this sequence.
now range will be $\left|x_1\right|-x_2$ hence option (c) is correct.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.