If 68% of the data points are between 25 and 35, and assuming a normal distribution, which is often the case with large datasets, we can use the empirical rule (also known as the 68-95-99.7 rule).
For a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% falls within two standard deviations.
- Approximately 99.7% falls within three standard deviations.
Given that the mean is 30, and 68% of the data points are between 25 and 35, it suggests a standard deviation of 5.
Therefore, for 99.7% of the data, which is three standard deviations from the mean:
\[30 - 3 \times 5 = 30 - 15 = 15\]
\[30 + 3 \times 5 = 30 + 15 = 45\]
So, the values that include 99.7% of the data points are from 15 to 45.
