DISTRIBUTIONS THE NATURE OR SHAPE OF THE DATA

DISTRIBUTIONS: THE NATURE OR SHAPE OF THE DATA WITHIN ITS RANGE.

ESSENTIALS: DISTRIBUTION SHAPES (LOTS OF THEM , BUT WE WILL FOCUS ON THREE MAIN TYPES. ) Be able to explain what constitutes a distribution. Be able to identify Left, Right and Normal distributions (and a Uniform distribution). Be able to determine if a distribution is normally distributed or skewed through use of a formula or computer software and, be able to interpret the results of this process.

DISTRIBUTIONS CAN OCCUR IN A NUMBER OF SHAPES INCLUDING: v Symmetric – a distribution is symmetric if the left half of the distribution is roughly a mirror image of its right half. v Skewed – a distribution is skewed if it is not symmetric and if it extends more to one side than the other v Uniform - Each value occurs in approximately the same amount.

THE SHAPE OF DISTRIBUTIONS Symmetric Distribution • A vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately mirror images. LARSON/FARBER 4 TH ED. 4

THE SHAPE OF DISTRIBUTIONS Skewed Left Distribution (negatively skewed) • The “tail” of the graph elongates more to the left. • The mean is to the left of the median. LARSON/FARBER 4 TH ED. Skewed Right Distribution (positively skewed) • The “tail” of the graph elongates more to the right. • The mean is to the right of the median. 5

THE SHAPE OF DISTRIBUTIONS Uniform Distribution (rectangular) • All entries or classes in the distribution have equal or approximately equal frequencies. • Symmetric. LARSON/FARBER 4 TH ED. 6

SYMMETRY n n Symmetry – a distribution is symmetric if the left half of the distribution is roughly a mirror image of its right half. Skewness – a distribution is skewed if it is not symmetric and if it extends more to one side than the other Mode = Mean = Median SYMMETRIC Mean Median Mode SKEWED LEFT (negatively) Mode Median Mean SKEWED RIGHT (positively)

Some Common Distribution Shapes