MGSC 291 Exam 16

descriptive statistics

collecting, organizing, summarizing, and presenting statistics

inferential statistics

drawing conclusions about a population based on data observed on a sample from that population

population

entire group of individuals

sample

subset of a population

parameter

µ, σ, π, number to describe a population

statistic

x̄, p̂, s, number to describe a sample, used to estimate the parameter

observational unit

unit upon which an observation is made

variable

characteristic of a observational unit

quantitative

numbers that have magnitude

qualitiative

categorical/factor, non-numeric or magnitudinal

discrete

counted

continuous

measured

nominal

no orderor

ordinal

inherent order

Tufte’s guidlines

graphical excellence (conveys message), visual integrity (display accurately and truthfully), data density (remove “chart junk”), aesthetic elegance (how simply does it convey a message)

summary of quantitative data

shape, central location, spread

central location

mean, median, modemea

mean

x̄, average, >mean (variable)

median

M, 50th percentile, middle of list, >median(variable)

mode

less stable than x̄ or M, typically used for factor data

spread

range, IQR, standard deviation, coefficient of variation

shape

skewness, kurtosis

range

max minus min, >range(variable)

IQR

Q3 minus Q1, middle 50%, >IQR(variable)

variance

average squared difference of observations from the mean, s², >var(variable)

standard deviation

the typical amount of deviation of data from x̄, >sd(variable)

coefficient of variation

standard deviation as a % of x̄, (SD/mean) X 100, compare variation with different units

skewness

degree of distortion from the bell curve, quantifies the amount of skewness and direction, 0-0.5 = fairly symmetric; 0.5-1 = moderately skewed, 1+ = highly skewedk

kurtosis

tailedness of the distribution, likelihood of having extreme values quantified

z score

allow comparison between different units of measurement with the same distribution, (observed value - mean / standard deviation)

empirical rule

only for normal distributions, 68%-95%-99.7%

chebyshevs theorem

for any distributions, 75% within 2 SD, 88.89% within 3 SD