Dec 5 B1 BW Chebyshev's Theorem

Front

What does the 'k' in Chebyshev's Theorem represent?

Back

The number of standard deviations from the mean.

Front

What is Chebyshev's Theorem?

Back

A statistical theorem that states that for any distribution, at least (1 - 1/k^2) of the values will fall within k standard deviations from the mean.

Front

If the mean of a distribution is 20 and the standard deviation is 2, what percent of values fall between 10 and 30 according to Chebyshev's theorem?

Back

At least 96%.

Front

How do you calculate the minimum percentage of data values within a certain range using Chebyshev's theorem?

Back

Use the formula: Minimum percentage = (1 - 1/k^2) * 100, where k is the number of standard deviations.

Front

What is the minimum percentage of data values that will fall within 2 standard deviations of the mean according to Chebyshev's theorem?

Back

At least 75%.

Front

If the mean age of salespeople is 30 years with a standard deviation of 6 years, what is the age range for at least 75% of the data?

Back

Between 18 and 42 years.

Front

What is the significance of Chebyshev's theorem in statistics?

Back

It provides a way to understand the spread of data in any distribution, regardless of its shape.

Front

If a distribution has a mean of 12 and a standard deviation of 2, what is the minimum percentage of data values that will fall between 4 and 20 trials?

Back

At least 93.75%.

Front

What does it mean if a distribution is 'skewed'?

Back

It means that the data is not symmetrically distributed, with a longer tail on one side.

Front

How can Chebyshev's theorem be applied in real-world scenarios?

Back

It can be used to assess the variability of data in fields like finance, education, and health.