lesson 9

The most widely known and used of all distributions.

A pattern for the distribution of a set of data that follows a bell-shaped curve.

Because it approximates many natural phenomena so well, it has developed into a standard of reference for many probability problems.

The graph of a normal distribution.

By varying the mean and standard deviation, we obtain different normal distributions; thus, there are an _____

Approximately 68% of observations lie _____ of the mean.

Approximately 95% of observations lie ______ of the mean (or between Mean +- 2 SD).

Approximately 99.7% of observations lie within 3 standard deviations of the mean.

a specific normal distribution that has a mean of 0 and a standard deviation of 1.

A ______ of 0 indicates that an observation is equal to the mean.

A frequency distribution is said to be symmetrical if the frequencies are equally distributed on both sides of the central value.

shape of symmetrical distribution

Frequencies first steadily rise and then steadily fall.

There is only one mode.

Mean = Median = Mode (or A.M = Median = Mode).

is a measure of the symmetry or asymmetry of a data distribution.

measures whether data is heavy-tailed or light-tailed in a distribution.

A distribution is ______ when its left and right sides are not mirror images.

A distribution is said to be _____ when the mean and the median fall at different points, and the balance (center of gravity) is shifted to one side or the other (left or right)

tell us the direction and the extent of skewness. The more the mean moves away from the mode, the larger the asymmetry or skewness.

Relationship: A.M = Median = Mode

right skewed

Relationship: A.M > Media > Mode

May include standard positive curves or 'L' shaped positively skewed curves

left skewed

Relationship: A.M < Median < Mode

May include standard negative curves or 'J' shaped negatively skewed curves.