5
QuizMultiple Select

Variation in Predictions and Estimates

Question 5 • Pre-Algebra B

Una was asked to write about predicting population means by taking the means of samples. She recorded a list of some statements generated from her classmates.Which statements are true? Select three choices.

Answer
A
The best prediction of the population mean is the value that falls between the least and greatest sample means.
B
It is unlikely that the population mean will be the least or greatest mean from the samples.
C
If the means of different samples are close in number, or have small variation, then they cannot be used to make predictions for the actual population.
D
A more accurate prediction of the population mean can be made by decreasing the number of random samples.
E
To find the range of the sample means, subtract the least value from the greatest value.

Explanation

Sample means tend to cluster around the population mean, so the population mean is likely to fall between the smallest and largest sample means (A), and it is unlikely to equal either extreme (B). The range is found by subtracting the least sample mean from the greatest sample mean (E). Small variation makes sample means more useful for prediction, not unusable, and taking more random samples generally improves a prediction—so C and D are false.

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