QuestionDescribe a distribution that is NOT normally distributed.
Studdy Solution
STEP 1
Assumptions1. A distribution is a set of data points.
. A normally distributed data set has a bell-shaped curve, also known as a Gaussian distribution.
3. The mean, median, and mode of a normally distributed data set are all equal and located at the center of the distribution.
4. In a normal distribution, approximately68% of the data falls within one standard deviation of the mean,95% falls within two standard deviations, and99.7% falls within three standard deviations.
STEP 2
A distribution that is not normally distributed can be described in several ways. One of the most common ways is by its skewness and kurtosis.
STEP 3
Skewness refers to the degree of asymmetry in the distribution. If the distribution is not symmetrical, it is said to be skewed. A positively skewed distribution has a long tail on the right, while a negatively skewed distribution has a long tail on the left.
STEP 4
Kurtosis refers to the "tailedness" of the distribution. A distribution with high kurtosis has heavy tails and a sharp peak, while a distribution with low kurtosis has light tails and a flat peak.
STEP 5
Another way to describe a distribution that is not normally distributed is by its lack of symmetry. A symmetric distribution can be folded along its mean and the two halves would match up. If this is not the case, the distribution is not symmetric and therefore not normally distributed.
STEP 6
A distribution that is not normally distributed could also have multiple modes, or peaks. A normal distribution has only one mode, located at the mean. If a distribution has more than one mode, it is not normally distributed.
STEP 7
Finally, a distribution that is not normally distributed could be described by its outliers. Outliers are data points that are significantly different from the other data points in the distribution. A normal distribution has few outliers, while a non-normal distribution may have many.
In conclusion, a distribution that is not normally distributed could be described as skewed, having high or low kurtosis, not symmetric, having multiple modes, or having many outliers.
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