STA 2023 Exam 1

the science of collecting, analyzing, interpreting, and presenting data

data that is describing using words or categories, qualitative

data that is describing using numbers, can be averaged

categorical and quantitative

bar charts (bars do not touch) and pie charts

histograms (bars usually touch), stem plots, box plots, and dot plots

center and spread

mean, median, mode

the 'average', the balancing point, distances from the data points always add up to zero

the middle ordered value, the 50th percentile, falls in (n+1)/2 position, always exactly 50% of the observations on either side of it and is not very sensitive to outlier, robust

the most frequently occurring number, the measure of center represents the most common observations or class of observations

range, variance, standard deviation, IQR

min-max, the measure of spread that is affected most by outliers

represents the 'typical' squared distance from the mean, in squared units, measure of spread around the mean, but its units are not the same as those of the data points

represents the 'typical' distance from the mean, in units of data, measure of spread that is smaller for distributions where the points are clustered around the middle, cannot be negative

interquartile range, Q3-Q1 where Q3= 75th percentile (the median of the 'top' half) and Q1= 25th percentile (the median of the 'bottom' half), gives the spread of the central (middle) 50% of the data set

any observations that are significantly far away from the rest of the data points

mean->median->mode

bell curve, mean=median=mode

mean<-median<-mode

mean=median

mean>median

mean=median

countable

measurable

vertical distance between the points and the line, sum to 0, error=actual-predicted

minimizes the sum of the residuals squared

slope, as x increases by 1, y is predicted to increase/decrease by b

y intercept, when x=0, y is predicted to be a

correlation coefficient, sign of the slope, measures strength and direction, between -1 and 1, not affected by units of x and y

coefficient of determination, percent of variation in y that is explained by x, between 0% and 100%, 1-r2= the fraction of the variation in y that is NOT explained by x, larger r2 is better

determined by the proportion of times the event(s) will occur in a long series of independent trials (law of large numbers)

P(not A) = 1-P(A)

equals 1 - none

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(A) + P(B)

P(A and B) = P(A) x P(B)

P(AlB) = P(A and B)/P(B) or P(BlA) = P(A and B)/P(A)

mutually exclusive, cannot occur together

occurrence of one does not affect the probability of the other

binompdf (n,p,x)

the condition is correctly determined to exist in the subject

the condition is correctly determined to not exist in the subject

the condition is incorrectly determined to exist in the subject

the condition is incorrectly determined to not exist in the subject

binomial and non binomial, RV's which assume a finite number of outcomes, countable, probability of an exact value can be computed

collection of yes/no (binary) outcomes

many types (distinguishing specific type is not required)

uniformly distributed and normally distributed, RV's which assume an infinite number of outcomes, measurable, probability of any exact value cannot be computed, probability is 0 (move on)

outcomes are equally likely

should be told the population is normal, z score can be used

a variable that represents the numerical outcome(s) of a random phenomenon

observation of binary, probability of success is constant, n fixed observations, n observations are independent, X~B(n,p)

two outcomes, mean and SD

three or more outcomes, mean

=mean=average

doesn't include x

doesn't include x

includes x

includes x

=(UV-LV)/(Max-Min)

probability, normalcdf(LV,UV,mean,SD), for z use 0 as mean and 1 as SD

value, invNorm(area to the left,mean,SD), for z use 0 as mean and 1 as SD