Standard Deviation & Chebyshev's Theorem Extra Practice

Front

What is the formula for calculating standard deviation?

Back

Standard Deviation (σ) = √(Variance)

Front

Given a variance of 64, what is the standard deviation?

Back

8

Front

What does Chebyshev's theorem state about data distribution?

Back

Chebyshev's theorem states that for any dataset, at least (1 - 1/k²) of the data values will fall within k standard deviations from the mean.

Front

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

Back

18 - 42 years

Front

Using Chebyshev's theorem, what is the minimum percentage of data values that will fall within 2 standard deviations from the mean?

Back

At least 75%.

Front

What is the k value for a range of 4 to 20 trials if the mean is 12 and the standard deviation is 2?

Back

4

Front

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

Back

At least 96%.

Front

What is the significance of the k value in Chebyshev's theorem?

Back

The k value represents the number of standard deviations from the mean.

Front

How do you calculate variance from standard deviation?

Back

Variance (σ²) = (Standard Deviation)².

Front

What is the minimum percentage of data values that will fall within 3 standard deviations from the mean according to Chebyshev's theorem?

Back

At least 88.89%.