Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 294 and standard deviation of 13.
95% of scores fall within the mean ± 2 SD. What does that tell you about your data?
The Empirical Rule, also known as the 68-95-99.7 Rule, states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Given a mean of 294 and a standard deviation of 13, we can use the Empirical Rule to find the range within which 95% of the data will fall.
Step 1: Calculate one standard deviation.
To find one standard deviation, we add and subtract the standard deviation from the mean:
294 + 13 = 307 (upper bound)
294 - 13 = 281 (lower bound)
Step 2: Calculate two standard deviations.
To find two standard deviations, we add and subtract twice the standard deviation from the mean:
294 + (2 * 13) = 320 (upper bound)
294 - (2 * 13) = 268 (lower bound)
Therefore, 95% of the data will fall between 268 and 320 for this data set with a mean of 294 and standard deviation of 13, according to the Empirical Rule.