Question

1. Which of these are random variables:

Population mean, sample mean, population variance, sample variance, population standard deviation, sample standard deviation, population range, sample range

2. Does variance matter? I have two routes to my work. Travel time on the first route takes me on average 20 minutes, and the second route 19 minutes. The standard deviation of travel time on the first route is 1.5 minutes, on the second is 5 minutes. Which route should I take?

Answer 1

1.Sample mean, sample variance, sample standard deviation and sample range are random variables.

Because its value depends on what the particular random sample happens to be. The expected value of the sample mean is the population mean, The sample variance, s2, is used to calculate how varied a sample is. A sample is a select number of items taken from a population. Standard error of the sample mean is the standard deviation of the population, divided by the square-root of the sample size. Also range is the spread (distance or value) from the lowest to the highest value in the sample. Thus all statistics are depends on sample which is randomly selected from population.

2.First route is best.

Because a small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another. And standard deviation is the square root of variance. Standard deviation of second root is larger than first route. That means this route involves some outlier like heavy traffic. If we choose second route due to it's minimum time we will get too late. So second route is not good for travell and thus variance does matter.