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

## Solution :

In the 2n observations, half of them equals a and remaining half equal -a. Then, the mean of total 2n observations is equal to 0.

$$\therefore$$   SD = $$\sqrt{\sum(x – \bar{x})^2\over N}$$

$$\implies$$  4 = $$\sum{x^2}\over 2n$$

$$\implies$$  4 = $$2na^2\over 2n$$

$$\implies$$  $$a^2$$ = 4

$$\therefore$$   a = 2

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