Explain how Tchebysheff's theorem can be used to help describe ...

[corkyiscool3328]

Explain how Tchebysheff's theorem can be used to help describe data in a population or a sample.
 
  What will be an ideal response?

Question 2

A direct retailer that sells clothing on the Internet has two distribution centers and wants to determine if there is a difference between the proportion of customer order shipments that contain errors (wrong color, wrong size, etc.).
 
  It takes a sample of orders from each distribution center and obtain the following results: Distribution Center 1 Distribution Center 2Number of orders 120 145Number of errors 4 6Based on these data it can proceed with assuming the normal distribution for each of the proportion sampling distributions. Indicate whether the statement is true or false

[amcvicar]

Answer to Question 1

If the data in a sample or a population are known to be bell-shaped, the empirical rule can be used to help us describe the data. However, when the sample or the population is not bell-shaped, Tchebysheff's theorem is very useful. It is a conservative theorem because it applies to any distribution. If we know the mean and standard deviation, Tchebysheff tells us that at least 75 percent of the data values will fall with  2 standard deviations of the mean and at least 88 percent will lie within 3 standard deviations of the mean. Keep in mind that in most instances, the percentage of observations will exceed these minimum amounts, but at least it gives us some idea of how the data are distributed without actually looking at all the data.

Answer to Question 2

FALSE