THE NORMAL CURVE
SHAPES OF DISTRIBUTIONS
Rectangular Distribution
Bimodal Distribution
When examining data using a histogram, we can refer to the overall appearance of the histogram as the shape of the distribution of the data. Certain shapes of distribution of data are more common then others and have special names.
Bell-shaped Distribution
Skewed Distribution
A bell-shaped distribution may be modeled with a normal curve (bell curve), which is the main focus of this lesson.
The extreme values on the right tend to increase the value of the mean so that it is larger than the median.
https://www.mathsisfun.com/data/standard-normal-distribution.html
Approximately 95% of all the data fall within 2 standard deviations of the mean.
EMPIRICAL RULE
Approximately 99.7% of all the data fall within 3 standard deviations of the mean.
https://www.mathsisfun.com/data/standard-normal-distribution.html
Two nonadjacent values occur more frequently than any others.
Has more of a "tail" on one side or the other
Skewed to the left
Has more of a "tail" on one side or the other.
Skewed to the right
The graph of a normal distribution is called a
NORMAL CURVE
The extreme values on the left tend to decrease the value of the mean so that it is less than the median.
mean < median
In any normal distribution,
Approximately 68% of all the data fall within 1 standard deviation of the mean.
PROPERTIES
OF A
NORMAL
DISTRIBUTION
All observed values occur with approximately the same frequency.