Question

One dataset has average = 15 and standard deviation =3. At least what percentage of records in the dataset have values between 9 and 21 (Hint: Even we have no access to this dataset, we can still conclude this.)?

O 95%
O 88%
O 90%
O 75%

Answer 1

Using Chebyshev's Rule, we can conclude that at least 75% of records in the dataset have values between 9 and 21, as this range encompasses two standard deviations from the mean.

Step-by-step explanation:

The question asked is, "At least what percentage of records in the dataset have values between 9 and 21 if the average is 15 and the standard deviation is 3?" To answer this, we can apply Chebyshev's Rule and the Empirical Rule, both of which deal with the spread of data in a dataset.

The range from 9 to 21 is two standard deviations away from the mean on both sides (15 - 3 × 2 = 9; 15 + 3 × 2 = 21). According to the Empirical Rule, for a bell-shaped and symmetric distribution, at least 95% of the data lies within two standard deviations of the mean. However, if we don't assume the distribution is bell-shaped or normal, we need to apply Chebyshev's Rule, which guarantees that at least 75% of data is within two standard deviations of the mean, regardless of the distribution shape.

Based on the information given and Chebyshev's Rule, we can confidently state that at least 75% of the records in the dataset have values between 9 and 21.