Question

at least 93.75% of the data in any data set lie within how many standard deviations of the mean? explain how you arrived at your answer.

explain how the number of standard deviations could be found for any data set. choose the correct answer below.

a. use chebyshevs theorem.
b. use the empirical rule.
c. use the coefficient of variation.

Explanation:

Identify the applicable theorem

Using the Chebyshevs Theorem knowledge point

$$ 1 - \frac{1}{k^2} \ge 0.9975 $$

Solve for the number of standard deviations

Using the Chebyshevs Theorem knowledge point

$$
LATEXBLOCK0
$$

Determine the method for any data set

Using the Chebyshevs Theorem knowledge point

• Chebyshev's Theorem applies to any data set regardless of the shape of the distribution.
• The Empirical Rule only applies to bell-shaped (normal) distributions.
• Therefore, to find the number of standard deviations for any data set, we must use Chebyshev's Theorem.

Answer:

Question 1

20

Question 2

• A. Use Chebyshev's Theorem. (Correct answer)
• B. Use the Empirical Rule.
• C. Use the Coefficient of Variation.