Dec 5 B4 BW Chebyshev's Theorem

Front

What is Chebyshev's Theorem?

Back

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

Front

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

Back

The number of standard deviations from the mean.

Front

If the mean is 30 and the standard deviation is 6, what is the range for at least 75% of the data according to Chebyshev's Theorem?

Back

18 - 42 years.

Front

How do you calculate the minimum percentage of data 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 from the mean.

Front

What is the minimum percentage of data values that will fall within 4 to 20 trials if the mean is 12 and the standard deviation is 2?

Back

93.75%.

Front

What is the significance of the standard deviation in Chebyshev's Theorem?

Back

It measures the dispersion of data points from the mean.

Front

If a distribution has a mean of 20 and a standard deviation of 2, what percent of values will fall between 10 and 30?

Back

At least 96%.

Front

What is the formula to find the range of data values using Chebyshev's Theorem?

Back

Range = Mean ± k * Standard Deviation.

Front

What does it mean if k = 2 in Chebyshev's Theorem?

Back

At least 75% of the data values lie within 2 standard deviations from the mean.

Front

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

Back

It can be used to understand the spread of data in various fields such as finance, education, and health.