distributions Flashcards
What is a normal distribution?
A normal distribution is a symmetrical, bell-shaped distribution where most of the data points cluster around the mean, with fewer points as you move away from the center.
What are the characteristics of a normal distribution?
The characteristics of a normal distribution include symmetry, with the mean, median, and mode all being equal, and the data points are spread in a predictable pattern around the mean.
What is a skewed distribution?
A skewed distribution is one where the data points are not symmetrically distributed around the mean, leading to a longer tail on one side of the distribution.
What are the characteristics of a positively skewed distribution?
In a positively skewed distribution, the tail on the right side is longer, and most data points are concentrated on the left side of the distribution. The mean is higher than the median.
What are the characteristics of a negatively skewed distribution?
In a negatively skewed distribution, the tail on the left side is longer, and most data points are concentrated on the right side of the distribution. The mean is lower than the median.
What is the shape of a normal distribution curve?
The shape of a normal distribution curve is bell-shaped and symmetrical, where the highest point of the curve is at the mean.
What is the difference between a normal distribution and a skewed distribution?
A normal distribution is symmetrical, with the mean, median, and mode being equal, while a skewed distribution has a tail on one side, causing the mean and median to differ.
How does the mean, median, and mode compare in a normal distribution?
In a normal distribution, the mean, median, and mode are all equal and occur at the center of the distribution.
How does the mean compare to the median in a positively skewed distribution?
In a positively skewed distribution, the mean is greater than the median because the longer right tail pulls the mean to the right.
How does the mean compare to the median in a negatively skewed distribution?
In a negatively skewed distribution, the mean is less than the median because the longer left tail pulls the mean to the left.
When is a normal distribution commonly used in statistics?
A normal distribution is commonly used in statistics when data is symmetrically distributed and can be approximated by a bell-shaped curve, such as human heights or test scores.
What is the range of standard deviations in a normal distribution?
In a normal distribution, approximately 68% of data lies within one standard deviation of the mean, 95% lies within two standard deviations, and 99.7% lies within three standard deviations.
What is the significance of skewness in a distribution?
Skewness indicates the direction of the tail in a distribution, which helps identify whether the data is concentrated on one side and whether statistical assumptions like normality are met.
What is a strength of using a normal distribution in statistical analysis?
A strength of using a normal distribution is that it allows for the use of parametric statistical tests, which are based on assumptions about the data’s normality.
What is a limitation of using a normal distribution in statistical analysis?
A limitation is that real-world data may not always follow a normal distribution, and using these methods may lead to incorrect conclusions if the data is skewed or has outliers.
How does a positively skewed distribution affect the mean and median?
In a positively skewed distribution, the mean is pulled to the right of the median, as the long tail on the right side increases the mean’s value.
How does a negatively skewed distribution affect the mean and median?
In a negatively skewed distribution, the mean is pulled to the left of the median because the long tail on the left side decreases the mean’s value.
How can you identify a skewed distribution visually?
A skewed distribution can be identified visually by the asymmetry of the curve, where one tail is longer than the other. The direction of the skew (positive or negative) depends on which tail is longer.
