Question

What happens when the sample size of an online poll is increased?

The variability increases
The variability decreases
The bias increases
The bias decreases
None of the above

Answer 1

As the sample size increases the standard deviation of the sample decreases and hence the variability of the sample decreases.

Hence the second option is the correct option.

Explanation:

i) let the standard deviation of the population be given by σ.

ii) for sample taken from among the population of size n the standard deviation of the sample becomes
`(\sigma)/(√(n) )` and so we can see that for the sample the standard deviation of the sample is less than the standard deviation of the sample.

iii) As the sample size increases we can say that the standard deviation of the sample decreases.

iv) the variance , or variability, of a sample is equal to the square of the standard deviation of the sample.

therefore as the sample size increases the standard deviation of the sample decreases and hence the variability of the sample decreases.