Before a sample variance is a good approximation of the population variance, what is needed?

Before a sample variance is a good approximation of the population variance, what is needed?

• A. A single observation
• B. The population mean
• C. A fairly large number of observations
• D. A small sample size

Answer: (C)

The estimate of population variance improves with more data. The sample variance comes from deviations around the sample mean, which itself is an estimate of the true population mean. With only a few observations, both the center and the spread are poorly defined, so the variance estimate can swing a lot from one sample to the next. As the number of observations grows, the sample mean gets closer to the true mean and the distribution of observed values around that mean better represents the population’s variability, so the calculated variance becomes a more reliable reflection of the population variance. In practical terms, you need a fairly large number of observations to obtain a good approximation. A single observation can’t reveal any spread, a small sample gives highly variable variance estimates, and simply knowing the population mean isn’t enough to determine variance.

The estimate of population variance improves with more data. The sample variance comes from deviations around the sample mean, which itself is an estimate of the true population mean. With only a few observations, both the center and the spread are poorly defined, so the variance estimate can swing a lot from one sample to the next. As the number of observations grows, the sample mean gets closer to the true mean and the distribution of observed values around that mean better represents the population’s variability, so the calculated variance becomes a more reliable reflection of the population variance. In practical terms, you need a fairly large number of observations to obtain a good approximation. A single observation can’t reveal any spread, a small sample gives highly variable variance estimates, and simply knowing the population mean isn’t enough to determine variance.