AP Statistics (Formulas) Flashcards

14023947275	Mean	Sum of observations/Number of Observations	0
14023947276	IQR	Q3-Q1 Resistant to outliers	1
14023947277	Standard Deviation	Common measure of spread. How far each observation is from the mean. Found with an average of the squared distances. Then taking the squared root. Avg squared distance: VARIANCE Square root of Var: STANDARD DEV	2
14023947278	Measures of Position	Percentiles: Percentile tells us a data point's position relative to other points in the data set. 85% (then that student scored higher than 85% of the students taking the SAT). Z-scores: Tells us a data point's position relative to the mean and measured in "standard" units or in standard deviations.	3
14023947279	Density Curve	Math model for a distribution. Shows the overall pattern of a distribution via a smooth curve, ignoring minor irregularities and outliers.	4
14023947280	Area under curve	Relative frequency of values in distribution. Always on or above horizontal axis. Total area underneath curve is exactly one.	5
14023947281	Mean + Median for Density Curve	Median of a density curve: Equal-areas point, the point that divides the area under the curve in half. Mean of a density curve: Balance point, at which the curve would balance if made of solid material. Median + Mean: Same for symmetric density curve, both lie at center Mean of skewed curve: Pulled away from median in direction of tail. Median is not at peak, but not affected by skew.	6
14023947282	Transforming Data	Mean: Changes when added to, also when multiplied Median: Changes when added to, also when multiplied Range/IQR: Does not change when addition, changes when multiplied St. Dev: Doesn't change when addition, changes when multiplied	7
14023947283	Normal Distribution	All: Symmetric, single-peaked, bell-shaped Described with Mean, Standard deviation Low standard deviation = high peak Mean= center Standard deviation= center of inflection point Describes as: APPROXIMATELY NORMAL	8
14023947284	Assessing Normality	#1 Histogram or stemplot: Test symmetry, bell-shaped #2 Empirical Rule (68%-95%-99.7%) Find the intervals, check the number and percent of data that appears within standard deviations from the sample mean. #3 Normal Probability Plot Found in Plot 1. Check if it is linear or not.	9
14023947285	Expected Value of Discrete Random Variable (Mean)	Ux= E(X) = x1p1 + x2p2..... Multiply each probability with the value it represents. Add all. This gives equal representation of values.	10
14023947286	Probability Distribution Standard Deviation	Var(x) = (X1-M1)^2p1 + ..... St Dev(X) = Root of Variance	11
14023947287	Binomial Formula	P(X=k) = P(exactly K successes in trial) = (Failure) (Success) Binompdf(n, p, k) for P(X=k) Bimocdf(n, p, k) for P(X<=k) 1-Binomcdf(n, p, k) for P(X<=k) = P(x>=k) n= # of attempts p= probability of success 1-p=1 = probability of failure k= number of successes	12
14023947288	BINOMIAL DISTRIBUTION RULE	If the sample is less than 10% of the population, can ignore issue of replacement. n< N/10 n= sample size N= population size	13
14023947289	Binomial Distribution SOCS	Shape: Depends of values of n, p Center: Mean=np Spread: Standard Dev= sqrt[ n * P * ( 1 - P ) ]	14
14023947290	Rule of Thumb for using normal distribution for the approximation of the binomial distribution	If np> 10 and n(1-p)10>10 It means it is approximately normal	15
14023947291	Geometric Formulas	P (x=k) = p (1-p) ^(k-1) P(x<=k) = p+ (1-p)p =(1-p)^2(p).... P(x>k)= 1-P(x<=k) Geompdf(p,k) = P(x=k) Geomcdf(p,k) = P(x<=k)	16
14023947292	Manipulating Normal Distributions	Random variable y=x+c Mean(y): Mean(x) + c Variance(y): Variance(x) Deviation(y): Deviation(x) Random variable z= bx Mean(z)= Mean(x) X b Variance(z)= Variance(z) X b^2 Deviation(z)= Deviation(w) X (abs value of b) Random variable w=bx+c Mean(w)=Mean(w) X b +c Variance(w)= Variance(w) X b^2 Deviation(w)= Deviation(w) X (abs value of b)	17
14023947293	Combining Probability Distributions	Mean(y-x)= Mean(y)-Mean(x) Standard Deviation(y-x)= Square root[ dev(x)^2 + dev(y)^2) ] Mean (x+y) = Mean(x)+Mean(y) Standard Deviation(x+y)= Square root[ dev(x)^2 + dev(y)^2) ]	18