For a set of data with mean 12 and variance 9, approsimately 68% of the values will fall between 6 to 18. Is the true or false and how do you find the answere?

Variance = SD^2

Therefore SD = 3

68% fall between ± 1 SD

What does that tell you?

False

The statement is true. To understand why, let's take a look at the concept of the empirical rule.

The empirical rule (also known as the 68-95-99.7 rule) is a guideline that applies to data that follows a bell-shaped, symmetrical distribution known as a normal distribution. According to this rule, approximately:

- 68% of the data falls within one standard deviation of the mean
- 95% falls within two standard deviations of the mean
- 99.7% falls within three standard deviations of the mean

Given that the mean is 12 and the variance is 9, we can determine the standard deviation using the formula: standard deviation = square root of variance.

In this case: standard deviation = √9 = 3.

Since 1 standard deviation represents 68% of the data, we can consider the range of values that fall within one standard deviation on either side of the mean.

Lower limit: 12 - 3 = 9
Upper limit: 12 + 3 = 15

Therefore, we can conclude that approximately 68% of the values will fall between 9 and 15, which is different from the range mentioned in the statement. Hence, the statement is false.

To find the correct answer, we need to use the range of values calculated based on the standard deviation, not the variance.