In a series of `2n` observations, half of them equal `a` end remaining half equal `-a.` If the S.D. of the observationsis `2,` then `|a|` equals (1) `

Question

In a series of `2n` observations, half of them equal `a` end remaining half equal `-a.` If the S.D. of the observationsis `2,` then `|a|` equals (1) `

In a series of `2n` observations, half of them equal `a` end remaining half equal `-a.` If the S.D. of the observationsis `2,` then `|a|` equals (1) `1/n` (2) `sqrt2` (3) `2` (4) `sqrt2/n`
A. `(1)/(n)`
B. `sqrt(2)`
C. `2`
D. `(sqrt(2))/(n)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
In the 2n observations, half of them equal to a and the remaining half equal to -a. Then the mean of total 2n observations is equal to zero. Therefore,
`S.D.=sqrt((sum(x-x)^(2))/(N))`
`2=sqrt((sum x^(2))/(2n))`
`implies 4 =(sum x^(2))/(2n) implies 4=(2a^(2))/(2n) implies a^(2)=4`
`implies |a|=2`

5 views Answered 2023-02-05 15:29