Unit `1 Review

Individuals

Individuals

objects described by a set of data; can be people, or animals or things

Variable

characteristics of an individual

Categorical variable

places an individuals into one of several groups or categories

Quantitative variable

takes numerical variables

Distribution

tells what values take the variable and how often it takes places

SOCS

Describes the overall pattern of a distribution

Spread - lowest and highest value

Outlier - unusual values

Center - approximate average

Shape - symmetry or skewed

Symmetric

Mean = Median

Skewed Left

Mean < Median

Skewed Right

Mean > Median

Mean

the average; add all the values and divide by the number of observations

Median

the midpoint

Five-number summary

Minimum, Q1, M, Q3, Maximum

Interquartile range (IQR)

Q3-Q1=IQR

Outlier Rule (using IQR)

Low outliers - Q1-1.5(IQR), High outliers - Q3 + 1.5(IQR)

Standard deviation

the average of the squares of deviations of the observations from their mean

Density Curve

describes the overall pattern of a distribution; always on or above the horizontal axis and has an area of 1 beneath it

Median of a density curve

the equal-areas point, the area under the curve in half

Mean of a density curve

the balance point

Normal distribution

a curve that is symmetric and based on a continuous variable

68-95-99.7 Rule

68% of the observations fall within 1σ of the mean μ, 95% of the observations fall within 2σ of the mean μ, and 99.7% of the observations fall within 3σ of the mean μ.

Z-score

the standardized value; used the formula z=x-μ/σ

Calculator functions

Inverse normal

x = μ+z(σ)