Using the Empirical Rule, between what two values will approximately 95% of the population be? The Empirical Rule states that approximately 95% of the data will be between
The correct answer and explanation is:
Correct Answer:
Approximately 95% of the data will be between two standard deviations below the mean and two standard deviations above the mean. This means:
Mean – 2(Standard Deviation) and Mean + 2(Standard Deviation)
Explanation:
The Empirical Rule is a statistical guideline that applies to data sets with a normal (bell-shaped) distribution. It provides an easy way to understand how data values are spread in relation to the mean (average).
According to the Empirical Rule:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean
Focusing on the 95% part, this rule tells us that nearly all values in a normally distributed population will be found within the interval defined by subtracting and adding two standard deviations from the mean. For example, if the mean test score in a class is 80 and the standard deviation is 5, then about 95% of students scored between:
80 − 2(5) = 70 and
80 + 2(5) = 90
So, approximately 95% of the scores lie between 70 and 90.
This rule is helpful in many real-life applications, such as quality control, grading exams, predicting outcomes, and analyzing patterns. It allows statisticians and analysts to quickly assess the spread and concentration of values within a dataset. However, the Empirical Rule assumes the data is symmetrically distributed and shaped like a bell curve. If the data is skewed or not normally distributed, this rule may not give accurate results.
In summary, when a dataset is normally distributed, around 95% of the population values lie between mean minus 2 standard deviations and mean plus 2 standard deviations.