ap stats midterm (unit 1-7)

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94 Terms

1

quantitative variable

numerical values

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2

categorical variables

takes on groups or labels

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3

association

knowing the value of one variable helps to predict the value of the other variable

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4

if there's no association, the bars should look ___________

the same

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5

what is a segmented bar graph

bars stacked to make 100%

<p>bars stacked to make 100%</p>
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6

what is a side by side bar graph

a graph where each bar represents the frequency or relative frequency for each group

<p>a graph where each bar represents the frequency or relative frequency for each group</p>
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7

what is a mosiac plot

a segmented bar graph where the bar width is proportional to the group size

<p>a segmented bar graph where the bar width is proportional to the group size</p>
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8

what do you use to describe distributions

S: shape

O: outliers

C: center (if skewed, use median) (if symmetric, use mean)

V: variability (IQR)

(remember to add context and use full sentences)

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9

how do you calculate range?

maximum-minimum

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10

what is standard deviation?

how much the data values typically vary from the mean

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11

is the median resistant or non resistant?

the median is resistant and not greatly effected by outliers

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12

are the mean and standard deviation resistant or non resistant?

mean and SD are non resistant, greatly effected by outliers

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13

how do you calculate outliers

lower outlier: Q1-1.5(IQR)

high outlier: Q3+1.5(IQR)

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14

what does teh 5 number summary consist of?

minimum, Q1, median, Q3, and maximum

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15

modified box plots show outliers as what symbol?

*

<p>*</p>
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16

what is a percentile?

the percent of data values less than or equal to a given value

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17

what is an ogive

a line graph that depicts cumulative frequencies (percentile).

Q1=25th percentile

med=50th percentile

Q3=75th percentile

<p>a line graph that depicts cumulative frequencies (percentile).</p><p>Q1=25th percentile</p><p>med=50th percentile</p><p>Q3=75th percentile</p>
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18

what is the purpose of a z score?

it tells you how many standard deviations above or below the mean a data value is

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19

what is the formula to calculate a z score?

value-mean/SD

<p>value-mean/SD</p>
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20

what is the empirical rule?

68-95-99.7

<p>68-95-99.7</p>
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21

what is an explanatory variable?

(X) is used to predict or explain

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22

what is a response variable?

(y) outcomes of the study/experiment

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23

how do you describe a scatterplot?

D: direction (+/-)

U: unusual features (gaps, clusters, outliers)

F: form (linear/nonlinear)

S: strength of correlation (weak, moderate, strong)

(remember to add context, doesn't need to be full sentences)

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24

what is correlation (r)?

tells you the direction and strength of the linear relationship

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25

interpret correlation (r)

the linear relationship between (x) and (y) is (strength) and (direction)

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26

interpret the coefficient of determination (r^2)

the (%) of variation in (y) can be explained by the linear relationship with (x).

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27

regression line

line of best fit.

y=a+bx

a= y int

b=slope

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28

interpret slope

for each additional (x), the predicted (y) (increases/decreases) by (slope).

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29

interpret and calulate residual

calculate: y-y hat (actual-predicted)

interpret: the actual (y) is (residual) (above/below) the predicted value.

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30

what is the LSRL

least squares regression line. it minimizes the sum of the squared residuals.

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31

how do outliers effect the LSRL?

horizontal: tilt the line

vertical: move line up or down

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32

what is a high leverage point?

point with large or small x values

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33

what point does the LSRL always pass through?

(x bar, y bar)

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34

what are the steps to a simple random sample?

1) label (assign random numbers)

2) randomize (random # generator)

3) select (find the thingsthat correspond to the #s)

*no repeats

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35

____________and ________________ are biased and don't represent the full population

convinient sample & voluntary response

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36

what is a stratified random sample?

a sample that split the population into groups (strata) and take the SRS from each group.

-each strata has individuals with similar characteristics

-stratify on a variable that will affect responses

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37

a good sampling method is _________ and _____________.

unbiased, low variability

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38

what is a systematic sample?

choosing a random starting point and using equal intervals. (EX: every 8th person)

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39

what is a cluster sample?

taking samples from SOME groups

<p>taking samples from SOME groups</p>
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40

what is a stratified sample?

taking some samples from ALL groups

<p>taking some samples from ALL groups</p>
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41

what is undercoverage?

when some members of the population can't be included in the sample

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42

what is nonresponse?

when an individual chosen for a sample doesn't respond or can't be reached

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43

what is response bias?

-bias in the wording of a question

-interviewer bias

-people lying

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44

what is an observational study?

overserving or using data that was already collected. no treatments are imposed

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45

what is an expiriment

something that can establish cause and effect and impacts treatments

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46

what's a confounding variable?

an outside variable that could influence the explanatory and response variables

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47

how do you design an experiment?

1) random assignment

2) replication (more than 1 in each group)

3) comparison (over 2 treatments)

4) control (other variables stay the same)

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48

how do you design random assignment?

1) label

2) randomize

3) assign

*shows causation

*minimizes confounding variables

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49

what is the placebo effect?

when a fake treatment (placebo) appears to work.

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50

what is a single blind experiment?

the experimenter knows, but the people being tested do not

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51

what is a double blind experiment?

when the subjects and experimenter both don't know the treatments

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52

what are blocks?

groups of subjects that are similar

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53

how do you do a randomized block design?

separate the subjects into blocks, ten randomly assign to treatments in each block.

*block on a characteristic that can impact results

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54

what is a matched pairs design?

the subjects are paired up and randomly assigned to treatments

*similar blocks of 2 OR each subject receives both treatments in a diff order

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55

what does it mean to be statistically significant?

when results of a study are too unusual to happen by chance. equal to or above 5%

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56

do larger samples have more or less accurate results?

more accurate

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57

should different samples give the same or different results?

different results

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58

in the short term, probabilities are...... (predictable or unpredictable)

unpredictable (the opposite is true as well)

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59

what is the law of large numbers?

if we do something many times, the proportion will approach the true probablity

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60

what is a simulation?

an imitation of chance behavior based on a model that accurately reflects the situation. (EX: flipping a coin, random # generator)

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61

describe the simulation process

1) describe how you will simulate one trial

2) perform many trials

3)use the results to answer the question

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62

what is a compliment?

the probability of an event NOT happening

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63

what is the formula for the probability of a compliment?

P(A^c)= 1-P(A)

<p>P(A^c)= 1-P(A)</p>
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64

what is a mutually exclusive(disjoint) event?

events that can't happen at the same time

*if mutually exclusive:

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

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65

what is a probability model?

-model that lists all possible outcomes and their probabilities.

-probabilities must add to 1

-all probabilities between 0-1

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66

If A and B are mutually exclusive....

P(A∩B)=0

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67

what is conditional probability?

given that A happened first, what are the chances of B also happening.

P(A/B)

*look at a specific row or column in table

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68

what does indepedent mean?

when knowing one event has or has not occurred, does not affect the probability of the second event.

if P(A)= P(A/B)= P(A/B^c) then A and B are independent

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69

what is the general multiplication rule?

P( A and B ) = P(A) P(B/A)

this is NOT on the formula sheet

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70

if A and B are independent....

P(A and B) = P(A) * P(B)

P(B)= P(B/A)

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71

how do you calculate the probability of "at least one"?

the probability of none

1-P(none)

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72

what is a discrete random variable?

a fixed number of values with gaps in between

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73

what does it mean if a value is continuous?

it has infinite values.

*density curves

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74

how do you multiply standard deviation

add variences and square root it

*don't +/- SD

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75

how do you determine is something is binomial?

B: binary (success and failure)

I: independent trials

N: number of trials is FIXED

S: same probability of success (p)

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76

what do k,p,n stand for?

k=number of successes

p=probability of success

n=number of trials

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77

when P(x=k)...

binompdf(n,p,k)

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78

P(x≤k)...

binomcdf(n,p,k)

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79

P (x>k)....

1-P(x≤k-1)

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80

what is the 10% condition?

when taking a sample w/o replacement we can still use a binomial distribution if your sample size is less than 10% of the population.

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81

if n times p is greater than 10 AND n (1-p) is greater than 10...

can use a normal distribution to approximate a binomial distribution

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82

how do you determine if geometric?

B: binary

I: independent

T: trials til success

S: same prob. of success

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83

in geometric problems, k represents...

the trial of the 1st success

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84

what is a parameter?

a number that describes a population

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85

what is a statistic?

a number that describes a sample

*use a statistic to estimate a parameter

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86

what is a sampling distribution

the distribution of a statistic

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87

what is an unbiased estimator?

when the mean of the sampling distribution is equal to population parameter

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88

what is a biased estimator?

when a statistic consistently overestimates the population parameter

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89

what is the relationship between sample size and variability?

as sample size increases, variability decreases

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90

what does a good statistic consist of?

1) low bias (randomizing)

2) low variability (big sample size)

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91

what condition must be met to use the standard deviation formula?

n is less than 10% of the population

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92

when is the sampling distribution approx. normal for sampling proportions?

n times p is greater than or equal to 10 AND (1-p) is greater than or equal to 10

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93

when is the sampling distribution approx. normal for sample means?

1) it's stated in the question

2) n is greater than or equal to 30 by the central limit theorem

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94

what is the central limit theorem (CLT)?

the sampling distribution of x bar is approx. normal when the sample size is large enough (n is greater than or equal to 30)

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