What Symmetric distribution is
In statistics, a symmetric distribution is a type of probability distribution in which the values of the random variables are distributed in a symmetric manner around the mean. This means that the probability of a value being higher or lower than the mean is the same. Examples of symmetric distributions include the normal distribution, the uniform distribution, and the binomial distribution.
Steps for Symmetric Distribution:
- Identify the type of distribution: Determine whether the data follows a symmetric, asymmetric, or bimodal distribution pattern.
- Calculate the mean: Find the average of the data set.
- Calculate the median: Find the midpoint of the data set (the value that is halfway through the data set when the values are sorted from lowest to highest).
- Calculate the mode: Find the most common value in the data set.
- Calculate the standard deviation: Measure the spread of the data from the mean.
- Calculate the skewness: Measure the asymmetry of the distribution by looking at the ratio of the third moment of the data to the third power of its standard deviation.
- Plot the data: Plot the data on a graph to visualize it.
- Evaluate the data: Compare the mean, median, mode, standard deviation, and skewness to determine if the data follows a symmetric, asymmetric, or bimodal distribution pattern.
Examples
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A bell-shaped curve is an example of symmetric distribution in statistics, where the mean, median, and mode are all equal.
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When the data is symmetrically distributed, the mean and median will be the same, and the data points will be equally distributed around the mean.
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In a symmetric distribution, the shape of the graph is the same on both sides of the mean, with no skewness.