AP STATISTICS : LOCK IN

How do you check if there is outliers?

calculate IQR; anything above Q3+1.5(IQR) or below Q1-1.5(IQR) is an outlier

If a graph is skewed, should we calculate the median or the mean? Why?

median; it is resistant to skews and outliers

If a graph is roughly symmetrical, should we calculate the median or the mean? Why?

mean; generally is more accurate if the data has no outliers

What is in the five number summary?

Minimum, Q1, Median, Q3, Maximum

Relationship between variance and standard deviation?

variance=(standard deviation)^2

variance definition

the variance is roughly the average of the squared differences between each observation and the mean

standard deviation

the standard deviation is the square root of the variance

What should we use to measure spread if the median was calculated?

IQR

What should we use to measure spread if the mean was calculated?

standard deviation

What is the IQR? How much of the data does it represent?

Q3-Q1; 50%

How do you calculate standard deviation?

1. Type data into L1

2. Find mean with 1 Variable Stats

3. Turn L2 into (L1-mean)

4. Turn L3 into (L2)^2

5. Go to 2nd STAT over to MATH, select sum(

6. Type in L3

7. multiply it by (1/n-1)

8. Square root it

What is the formula for standard deviation?

Categorical variables vs. Quantitative Variables

Categorical: individuals can be assigned to one of several groups or categories

Quantitative: takes numberical values

If a possible outlier is on the fence, is it an outlier?

No

Things to include when describing a distribution

Center (Mean or Median), Unusual Gaps or Outliers, Spread (Standard Deviation or IQR), Shape (Roughly Symmetric, slightly/heavily skewed left or right, bimodal, range)

Explain how to standardize a variable. What is the purpose of standardizing a variable?

Subtract the distribution mean and then divide by standard deviation. Tells us how many standard deviations from the mean an observation falls, and in what direction.

What effect does standardizing the values have on the distribution?

shape would be the same as the original distribution, the mean would become 0, the standard deviation would become 1

What is a density curve?

a curve that (a) is on or above the horizontal axis, and (b) has exactly an area of 1

Inverse Norm

when you want to find the percentile: invNorm (area, mean, standard deviation)

z

(x-mean)/standard deviation

pth percentile

the value with p percent observations less than is

cumulative relative frequency graph

can be used to describe the position of an individual within a distribution or to locate a specified percentile of the distribution

How to find and interpret the correlation coefficient r for a scatterplot

STAT plot, scatter, L1 and L2 (Plot 1: ON); STAT --> CALC --> 8:LinReg(a+bx)

No r? --> 2nd 0 (Catalog) down to Diagnostic ON

r

tells us the strength of a LINEAR association. -1 to 1. Not resistant to outliers

r^2

the proportion (percent) of the variation in the values of y that can be accounted for by the least squares regression line

residual plot

a scatterplot of the residuals against the explanatory variable. Residual plots help us assess how well a regression line fits the data. It should have NO PATTERN

regression line

a line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x.

residual formula

residual=y-y(hat) aka observed y - predicted y

What method do you use to check if a distribution or probability is binomial?

BINS:

1. Binary: There only two outcomes (success and failure)

2. Independent: The events independent of one another?

3. Number: There is a fixed number of trials

4. Success: The probability of success equal in each trial

What method do you use to check if a distribution or probability is geometric?

BITS:

1. Binary: There only two outcomes (success and failure)

2. Independent: The events independent of one another

3. Trials: There is not a fixed number of trials

4. Success: The probability of success equal in each trial

n

number of trials

p

probability of success

k

number of successes

Binomial Formula for P(X=k)

(n choose k) p^k (1-p)^(n-k)

Binomial Calculator Function to find P(X=k)

binompdf(n,p,k)

Binomial Calculator Function for P(X≤k)

binomcdf(n,p,k)

Binomial Calculator Function for P(X≥k)

1-binomcdf(n,p,k-1)

mean of a binomial distribution

np

standard deviation of a binomial distribution

√(np(1-p))

Geometric Formula for P(X=k)

(1-p)^(k-1) x p

Geometric Calculator Function to find P(X=k)

geometpdf(p,k)

Geometric Calculator Function for P(X≤k)

geometcdf(p,k)

Geometric Calculator Function for P(X≥k)

1-geometcdf(p,k-1)

Mean of a geometric distribution

1/p=expected number of trials until success

Standard deviation of a geometric distribution

√((1-p)/(p²))

What do you do if the binomial probability is for a range, rather than a specific number?

Take binomcdf(n,p,maximum) - binomcdf(n,p,minimum-1)

how do you enter n choose k into the calculator?

type "n" on home screen, go to MATH --> PRB --> 3: ncr, type "k"

μ(x+y)

μx+μy

μ(x-y)

μx-μy

σ(x+y)

√(σ²x+σ²y)

What does adding or subtracting a constant effect?

Measures of center (median and mean).

Does NOT affect measures of spread (IQR and Standard Deviation) or shape.

What does multiplying or dividing a constant effect?

Both measures of center (median and mean) and measures of spread (IQR and standard deviation).

Shape is not effected.

For variance, multiply by a² (if y=ax+b).

σ(x-y)

√(σ²x+σ²y) --> you add to get the difference because variance is distance from mean and you cannot have a negative distance

calculate μx by hand

X1P1+X2P2+…. XKPK (SigmaXKPK)

calculate var(x) by hand

(X1-μx)²p(1)+(X2-μx)²p(2)+…. (Sigma(Xk-μx)²p(k))

Standard deviation

square root of variance

discrete random variables

a fixed set of possible x values (whole numbers)

continuous random variables

-x takes all values in an interval of numbers

-can be represented by a density curve (area of 1, on or above the horizontal axis)

What is the variance of the sum of 2 random variables X and Y?

(σx)²+(σy)², but ONLY if x and y are independent.

mutually exclusive

no outcomes in common

addition rule for mutually exclusive events

P (A U B)

P(A)+P(B)

complement rule

P(A^C)

1-P(A)

general addition rule (not mutually exclusive)

P(A U B)

P(A)+P(B)-P(A n B)

intersection

P(A n B)

both A and B will occur

conditional probability

P (A | B)

P(A n B) / P(B)

independent events (how to check independence)

P(A) = P(A|B)

P(B)= P(B|A)

multiplication rule for independent events

P(A n B)

P(A) x P(B)

general multiplication rule (non-independent events)

P(A n B)

P(A) x P(B|A)

sample space

a list of possible outcomes

probability model

a description of some chance process that consists of 2 parts: a sample space S and a probability for each outcome

event

any collection of outcomes from some chance process, designated by a capital letter (an event is a subset of the sample space)