Answer :
In a normally distributed dataset, the true statement is: "The 68-95-99.7 rule can be used." Let's explore why this is the correct statement:
1. Normally Distributed Dataset:
- A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, where most of the observations cluster around the central peak.
2. Mean, Median, and Mode:
- In a perfectly normal distribution, the mean, median, and mode are all equal. Therefore, statements like "Its mean is larger than the median" or "Its mode is larger than the mean" are not true for a normal distribution.
3. 68-95-99.7 Rule (Empirical Rule):
- This rule is specific to normal distributions and provides a way to understand the spread of data.
- Approximately 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.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
- This makes the rule a true characteristic of a normal distribution.
4. Standard Deviation:
- If the standard deviation were 0.0, it would mean all data points are exactly at the mean, which is not a typical characteristic of a normally distributed dataset.
Based on these explanations, the statement "The 68-95-99.7 rule can be used" is indeed the true statement about a normally distributed dataset.
1. Normally Distributed Dataset:
- A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, where most of the observations cluster around the central peak.
2. Mean, Median, and Mode:
- In a perfectly normal distribution, the mean, median, and mode are all equal. Therefore, statements like "Its mean is larger than the median" or "Its mode is larger than the mean" are not true for a normal distribution.
3. 68-95-99.7 Rule (Empirical Rule):
- This rule is specific to normal distributions and provides a way to understand the spread of data.
- Approximately 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.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
- This makes the rule a true characteristic of a normal distribution.
4. Standard Deviation:
- If the standard deviation were 0.0, it would mean all data points are exactly at the mean, which is not a typical characteristic of a normally distributed dataset.
Based on these explanations, the statement "The 68-95-99.7 rule can be used" is indeed the true statement about a normally distributed dataset.
