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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.

Mean

Median

Mode

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

The normal curve is

BELL-SHAPED

In any normal distribution,

Approximately 68% of all the data fall within 1 standard deviation of the mean.

Symmetry

50%

PROPERTIES

OF A

NORMAL

DISTRIBUTION

Symmetric about the mean

Mean = Median = Mode

All observed values occur with approximately the same frequency.

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