normal distribution left-skewed distribution right-skewed distribution skewed distribution

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Let's break down the different types of distributions you've mentioned: 1. **Normal Distribution**: - A normal distribution is a symmetric, bell-shaped distribution characterized by its mean (μ) and standard deviation (σ). - The mean, median, and mode of a normal distribution are all equal and located at the center of the distribution. - Approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations (this is known as the empirical rule). 2. **Left-Skewed Distribution (Negative Skew)**: - A left-skewed distribution has a longer tail on the left side of the distribution. - In this type of distribution, the mean is typically less than the median, which is less than the mode (mean < median < mode). - This indicates that there are a few low values that pull the mean down, while most of the data is concentrated on the right. 3. **Right-Skewed Distribution (Positive Skew)**: - A right-skewed distribution has a longer tail on the right side of the distribution. - In this case, the mean is typically greater than the median, which is greater than the mode (mean > median > mode). - This suggests that there are a few high values that pull the mean up, while most of the data is concentrated on the left. 4. **Skewed Distribution**: - A skewed distribution is any distribution that is not symmetric and has a tail on one side. - It can be either left-skewed or right-skewed, depending on the direction of the tail. - Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. ### Summary: - **Normal Distribution**: Symmetric, bell-shaped, mean = median = mode. - **Left-Skewed Distribution**: Longer left tail, mean < median < mode. - **Right-Skewed Distribution**: Longer right tail, mean > median > mode. - **Skewed Distribution**: General term for any non-symmetric distribution, can be left or right skewed. If you have any specific questions or need further details on any of these distributions, feel free to ask! **Distributions Explained:** 1. **Normal Distribution**: - Symmetrical, bell-shaped curve. - Mean, median, and mode are all equal. - About 68% of data is within one standard deviation from the mean. 2. **Left-Skewed Distribution (Negative Skew)**: - Longer tail on the left. - Mean < median < mode. 3. **Right-Skewed Distribution (Positive Skew)**: - Longer tail on the right. - Mean > median > mode. 4. **Skewed Distribution**: - Any non-symmetric distribution, can be left or right skewed. **Summary:** - **Normal**: Symmetrical with equal mean, median, and mode. - **Left-Skewed**: Longer left tail with mean less than median. - **Right-Skewed**: Longer right tail with mean greater than median. - **Skewed**: Any distribution that is not symmetric. If you have more questions, feel free to ask!

normal distribution left-skewed distribution right-skewed distribution skewed distribution

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