Three national news networks are trying to estimate what percentage of

American voters support a particular presidential candidate. To estimate the

population parameter, each of the three networks collect data from a simple

random sample of voters. Here are the numbers of voters in the networks

random samples:

• Network A: 1500 voters sampled

• Network B: 1250 voters sampled

• Network C: 1800 voters sampled

Which sample is likely to have the least variability?

O

A. The Network A sample

O

B. The Network B sample

O

C. The Network C sample

Option C. The Network C sample.

Explanation:

The variability of a sample may be described by using some common statistics like the variance and the standard deviation.

The variance and the standard deviation measure the difference between the values of the data and the mean. The variance is the average square of those differences or deviations. The standard deviation is the square root of the variance.

Thus, both variance and deviations, being an average of the differences of the data from the mean contain the number of data in the denominator of the equation.

That lets you know to conclude that the larger the number of data (the larger the sample) the smaller the variance and the standard deviation, this is the lower the variability of the data.

Hence, Network C, which has the greatest number of voters sampled (1,800) is likely to have the least variability.