Inspecting Distribution

Distributino f variable tells us what values it takes and how often it takes these values. When examining distribution, look for shape, center, and spread and for clear deviations from the overall shape. Modes is another aspect of overall shape.

Overall pattern by giving numerical measures of center and spread, and a verbal description of shape

Mean and Standard Deviation -> Symmetric Distribution Five-Number Summary -> Skewed Distribution Recognize Outliers

To measure center -> find the mean of a set of observations and find the median of a set of observations. Median is more resistant, or less affected by extreme observations than the mean. The skewness in a distribution moves the mean away from the median toward the long tail.

Nummerical summary of a distribution should include center, spread, and variability. The mean and the median describe the center of a distribution in different ways. Mean is the average of the observations, and the median is the midpoint of the values.

When using the median to indiciate center, describe its spread by giving the quartiles. An extreme observation is an outlier if it is smaller than Q1-(1.5*IQR) or Q3+(1.5*IQR)

The five number summary consists of the median, the quartiles, the high and low extremes, and a quick overall description of the distribution. Median describes the center, the quartiles and extremes show the spread.

Variance is S^2. Square root of variance is the standard deviation. They are measurements of spread about the mean as center. Standard deviation is zero when there is no spread and gets larger as the spread increases. Quartiles are resistant but the standard deviation is not.