Stats Definitions

Statistics

Statistics

deals with the collection, organization, presentation, analysis, and interpretation of data

Probability

measures the certainty or uncertainty that an event will happen.

Random Variable

is normally denoted by the uppercase (X) variable.

Classifications of Random Variable

Discrete and Continuous

Discrete Random Variable

can only take integral values, these are values obtained by counting.

Continuous Random Variable

can take any value within a range of values, these are values obtained by measuring.

Probability Distribution

A rule or a set of rules that assigns probabilities to values of a random variable.

Mean

expected value; denoted by E(X)

Formula: E(X) = ∑ (Xi •P(Xi))

Average

Variance

measures its spread; denoted by Var(X) or σ2

Formula: Var(X) = ∑ (Xi - E(X))2 •P(Xi))

Normal Distribution

• very common probability model on probability distribution

for a continuous random variable X

• also known as the Gaussian Distribution or X-Distribution

Statisticians who contributed

o C.F. Gauss

o A. de Moivre

o P.S. Laplace

o R. Adrian

Shape, Center, Spread

Each normal distribution has a similar _______ but each one is different in terms of its ________ and its _______.

Center, Mean, μ, Spread, Variance, σ²

The _______ is measured by the _______, denoted as ___. Each normal distribution has its own _______, measured by the ________, denoted as ___.

Standard Deviation, σ

The distance from the mean out to either saddle point is equal to ________, denoted as _________.

Bell shaped

The distribution curve of a normal distribution is _______.

Symmetrical

The curve is __________ about its center.

Equal

The mean, the median, and the mode of a normal distribution are ________.

1

The area under the curve is equal to _____. Thus, it represents the probability or proportion or percentage associated with the specific sets of measurement values

Denser, Less Dense

Normal distributions are _______ in the center and ________ in the tails.

Width

The _______ of the curve is determined by the standard deviation of the distribution.

68.2% (34.1% + 34.1%)

95.4%(13.6%+13.6%)

99.7%(2.15%+2.15%)

0.3%

Area of:

1 SD =

2 SD =

3 SD =

Tails =

0 and 1

a normal probability distribution that has a mean μ = ___ a standard deviation = ___.

Standard Normal Distribution

also known as Z-Distribution or Special Normal Distribution