In a series of 2n observations, half of them equal a and remaining half equal -a. If the standard deviation of the observations is 2, then |a| equals - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

1 attempts0% success rate3 marks (−1)

In a series of 2 n observations, half of them equal a and remaining half equal - a . If the standard deviation of the observations is 2, then ∣ a ∣ equals

Solution & Step-by-step Explanation

The mean of the 2 n observations is \overset{x}{ˉ} = \frac{n ( a ) + n ( - a )}{2 n} = 0 . Standard Deviation σ = \frac{\sum x _{i}^{2}}{N} - \overset{x}{ˉ}^{2} . Given σ = 2 : 2 = \frac{n ( a ^{2} ) + n ( - a ) ^{2}}{2 n} - 0^{2} . 2 = \frac{2 n a ^{2}}{2 n} = a^{2} = ∣ a ∣ . Thus, ∣ a ∣ [c i t e_{s} t a r t] = 2 .

Try it yourself before checking the explanation above.

In a series of 2 n observations, half of them equal a and remaining half equal - a . If the standard deviation of the observations is 2, then ∣ a ∣ equals

\frac{1}{n}

2

2

\frac{2}{n}

Practice with timed mock tests and track your performance across Mathematics.