Understanding Chebyshev's Theorem

What is the main difference between Chebyshev's Theorem and the Empirical Rule?

• Chebyshev's Theorem applies to bell-shaped data only.

• The Empirical Rule provides exact percentages for any data shape.

• The Empirical Rule is more accurate for non-bell-shaped data.

• Chebyshev's Theorem applies to non-bell-shaped data.

According to Chebyshev's Theorem, what is the minimum percentage of data within two standard deviations?

• 95%

• 75%

• 88.9%

• 68%

What is the formula used in Chebyshev's Theorem to calculate the minimum percentage of data within K standard deviations?

• 1/K

• 1 - 1/K^2

• 1 - 1/K

• 1/K^2

In Chebyshev's Theorem, what does the variable 'K' represent?

• The number of standard deviations from the mean

• The standard deviation

• The mean of the dataset

• The percentage of data within the range

For a non-bell-shaped distribution, what does Chebyshev's Theorem guarantee for data within three standard deviations?

• At least 99.7% of data

• At least 88.9% of data

• At least 75% of data

• At least 68% of data

In a dataset with a mean of 34,200 and a standard deviation of 2,200, what percentage of data lies between 29,800 and 38,600 according to Chebyshev's Theorem?

• At least 68%

• At least 88.9%

• At least 75%

• At least 95%

What is the significance of the phrase 'at least' in Chebyshev's Theorem?

• It indicates the exact percentage of data.

• It provides a maximum limit for data distribution.

• It is irrelevant to the theorem's application.

• It suggests a minimum percentage of data within the range.

For a dataset with a mean of 230 and a standard deviation of 58, what percentage of data lies between 56 and 404 according to Chebyshev's Theorem?

• At least 95%

• At least 88.9%

• At least 75%

• At least 68%

Why is Chebyshev's Theorem considered a conservative estimate?

• It overestimates the percentage of data within standard deviations.

• It is only applicable to small datasets.

• It gives a lower limit for data distribution.

• It provides exact percentages for bell-shaped data.

Which of the following is true about Chebyshev's Theorem?

• It is applicable to any data shape, providing a minimum percentage.

• It provides a precise percentage for any data distribution.

• It is more accurate than the Empirical Rule for bell-shaped data.

• It is only useful for data with a known distribution shape.