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2020 AP STATISTICS CONCEPT MASTERY > LIFE LINE CONCEPT TEST > Flashcards

LIFE LINE CONCEPT TEST Flashcards

1
Q

How do you describe CENTER for bimodal or multimodal?

A

talk about the modes (the lumps, the clusters)

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2
Q

Interpret r squared

A

r squared % of variability in y can be explained by the model with x. The rest is in residuals…

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3
Q

How are mean, median and mode positioned in a skewed left histogram?

A

goes in that order, mean median mode

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4
Q

When drawing a normal model, what are the PERCENTILES from left to right?

A

2.5, 16, 50, 84, 97.5

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5
Q

Give an example of independent variables

A

If 80% prefer cheese and only 20% prefer pepperoni IN EACH GRADE AT BHS…then they all have the same preference, so grade doesn’t matter. We say “school year and pizza choice are independent”

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6
Q

what is the LSRL

A

the “least squares regression line”
that line you plot
OR
That equation

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7
Q

How can you match boxplots to histograms?

A

USE THE FISH TANK METHOD!

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8
Q

If the mean is above the median, the distribution may be

A

skewed right… the mean follows the tail

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9
Q

mean/SD/median/IQR. How do I know which ones to use?

A

when unimodal and symmetric, mean and sd. If skewed or outliers? Median and IQR. If bimodal? Talk about the MODES

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10
Q

Interpret residual: Points below the line/negative resid

A

“the model overpredicted”
or
“Actual value was below the the expected (or predicted)”

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11
Q

What is a CUMULATIVE FREQUENCY GRAPH?

A

An OGIVE. It shows the added up totals as you go left to right.

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12
Q

not independent is the same as

A

associated

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13
Q

What point is on every regression line?

A

the mean-mean point. (x bar, y bar).
This point is generally not one of the points on the scatterplot.
Usually none of the scatterplot points are on the regression line.

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14
Q

Compare population to sample

A

populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.

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15
Q

When there is no relationship between two variables, we say they are

A

independent (or not associated)

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16
Q

If something is correlated is it associated?

A

Yes.
If it is correlated then it must be associated.
However, if it is associated,it may not be correlated.

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17
Q

Does the IQR capture 68% of the data?

A

NO. it catches the middle 50%.

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18
Q

What do OGIVES look like?

A

They all start at the bottom left (0%) and go to top right (100%)

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19
Q

which is response?

A

y variable,
the Vertical axis..
It “responds” to the x

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20
Q

where are the “outlier fences?”

A

1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.

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21
Q

If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?

A

Median (center) and IQR (spread)

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22
Q

What symbols do we use for population standard deviation and sample standard deviation?

A

Sigma for population and s for sample.

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23
Q

describe a scatterplot’s strength?

A

give the r value (if straight),
or say…
“tightly packed… loosely packed”

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24
Q

Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest.

A

I was curious about a population parameter, but a census was too costly so I decided to choose a sample, collect some data, calculate a statistic and use that statistic to make an inference about the population parameter (aka the parameter of interest).

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25
Q

Compare DATA-STATISTIC-PARAMETER using categorical example

A

Data are individual measures? like meal preference: ?taco, taco, pasta, taco, burger, burger, taco?? Statistics and Parameters are summaries. A statistic would be ?42% of sample preferred tacos? and a parameter would be ?42% of population preferred tacos.?

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26
Q

how do you describe direction?

A

positive or negative

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27
Q

How do you describe SPREAD for skewed distributions (or distributions with outliers?)

A

Use the IQR

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28
Q

What is meant by relative frequency?

A

The PERCENT of time something comes up (frequency/total)

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29
Q

Give a simple example showing that adding a constant doesn’t change the spread, but changes the center. (this always happens)

A

Data set: 1,2,3,4,5 Spread (range):4, Center: 3 add three and get new data set: 3,4,5,6,7 spread:4 Center: 5 (center went up, spread stayed the same). The IQR and SD will stay the same, but median and mean go up 3. Called shifting, or sliding the data.

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30
Q

How do you find the median from an OGIVE?

A

go halfway up the y axis, then shoot across to the curve, then straight down. It’s at the 50th percentile (halfway up)

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31
Q

What is the five number summary?

A

min, Q1 , Q2(median), Q3 and max

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32
Q

What is data?

A

Any collected information. Generally each little measurement? Like, if it is a survey about liking porridge? the data might be ?yes, yes, no, yes, yes? if it is the number of saltines someone can eat in 30 seconds, the data might be ?3, 1, 2, 1, 4,3 , 3, 4?

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33
Q

how do you describe form of a scatterplot?

A

straight orcurved?

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34
Q

What is a standard deviation?

A

average (typical) distance to the mean (about). It is how far you expect a random value to be away from the middle.

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35
Q

How do youinterpret slope EQUATION?

rSy/Sx

A

for each increase of 1 st dev in x direction,
you go r st dev in y direction.
2st dev in x, you go 2r st. devin y.
3st dev in x, you go 3r st. dev in y.

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36
Q

How do you find outliers in regression?

A

they don’tfollow the “flow”

pinky trick, cover with you pinky.. Then uncover.. Does it follow the flow?

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37
Q

What values can r be?

A

from -1 to +1

r near 0 is WEAK

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38
Q

What are the two types of observational studies?

A

Retrospective, and Prospective

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39
Q

What is variability?

A

Differences? how things differ. There is variability everywhere.. We all look different, act different, have different preferences? Statisticians look at these differences.

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40
Q

What should we look for in resid plot?

A

Curve or pattern means a linear model is NO GOOD.
Also, it should have equalish scatter from left to right
It should look RANDOM

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41
Q

What is extrapolation?

A

Making predictions outside of the x values you have.

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42
Q

What is a Z score?

A

The number of standard deviaiton away from the mean

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43
Q

What does normcdf do?

A

It gives you the area under the normal curve between any two z scores

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44
Q

If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and one of them had 9 pickles, then the number 9 from that burger would be calle

A

a datum, or a data value.

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45
Q

How do you describe CENTER for skewed or distributions with outliers?

A

use the MEDIAN

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46
Q

Association and Independence. How are they related?

A

Variables are either independent or associated. Meaning: if one impacts the other then we say there is an association. If not, Then they are independent.

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47
Q

Give a quick example of associated variables

A

A higher percentage of boys play video games than girls so we say “gender and video game playing are associated” or “gender and video game playing are not independent”

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48
Q

What is the difference between categorical VARIABLES and categorical DATA?

A

The Variable is the overall category. Like “EYE COLOR”. The data is the actual measurement from the subjects. Like “blue, brown, blue”

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49
Q

What is the IQR?

A

Interquartile range… a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.

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50
Q

what does influential mean?

A

It impacts the SLOPE.
It means that the point, when added or removed to data, will influence the SLOPE.
Generally these are outliers in the x direction. Far left or right.

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51
Q

what is leverage?

A

Far right or far left from the middle.
leverage just means it is far away from x-bar
Some leverage points are not influential if they go along with the flow of the scatter.

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52
Q

Compare DATA-STATISTIC-PARAMETER using quantitative example

A

Data are individual measures, like how long a person can hold their breath: ?45 sec, 64 sec, 32 sec, 68 sec.? That is the raw data. Statistics and parameters are summaries like ?the average breath holding time in the sample was 52.4 seconds? and a parameter would be ?the average breath holding time in the population was 52.4 seconds?

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53
Q

How do you describe a scatterplot?

A

DIRECTION
FORM
STRENGTH
and STRANGE

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54
Q

What is a residual?

A 
Vertical distance to the LSRL.
ACTUAL-PREDICTED,
A-P, like this class AP (get it?)
(observed-predicted)
Take y data found and from that, subtract the y you get from plugging the x into the model (equation).
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55
Q

What is the line that you plot?

A

IT IS A MODEL!

It is the LSRL and it is the model we are talking about

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56
Q

if you switch x and y does r change?

A

NO. The strength stays the same.

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57
Q

If I take a random sample 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and the average number of pickles was 9.5, then 9.5 is considered a _______?

A

statistic. (t is a summary of a sample.)

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58
Q

What is the difference between discrete and continuous variables?

A

Discrete can be counted, like “number of cars sold” they are generally integers (you wouldn’t sell 9.3 cars), while continuous would be something like weight of a mouse? 4.344 oz.

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59
Q

Which calculator function gives you a z score?

A

invnorm(%ile)

60
Q

What is a random sample?

A

When you choose a sample by rolling dice, choosing names from a hat, or other REAL RANDOMLY generated sample. Humans can’t really do this well without the help of a calculator, cards, dice, or slips of paper.

61
Q

Does r2 tell direction?

A

NO

r2 is always positive, so you can’t use it to see if the relationship is negative.

62
Q

Year in school (F,S,J,S) and Pizza Preference (pepperoni or cheese) are __________ because _______________

A

independent because all grades have similar preference distributions.. 40% cheese, 30%pepperoni, 20% veggie 10% other

63
Q

are any populations actually normal?

A

no, nothing is normal, just normalish. The only normal thing is the model we use.

64
Q

Lurking variable: Why are there more ice cream sales on days that there are more surfing accidents? Is the ice cream putting surfers at risk?

A

The WEATHER is the lurking variable.
When it is a nice day, more surfers and more ice creams are sold.
So, the WEATHER causes both to go up and down together.

65
Q

When there is a relationship between two variables, we say that they are

A

associated (or not independent)

66
Q

What is Statistics?

A

The study of variability

67
Q

For information purposes, which gives LEAST… stem-leaf, histogram or box-whisker?

A

Box/Whisker, BE CAREFUL. you really don’t know how things are distributed. The box and whisker and fish tank give a very GENERAL look.

68
Q

What is the total area under the normal curve?

A

1 or 1.000

69
Q

what is the emperical rule?

A

mean 68-95-99.7 yeah!

70
Q

What is frequency?

A

How often something comes up

71
Q

How can you describe spread?

A

range, IQR, stand dev, variance, or simply say: From here, to about here

72
Q

What is the difference between quantitative and categorical data?

A

The data is the actual gathered measurements. So, if it is eye color, then the data would look like this “blue, brown, brown, brown, blue, green, blue, brown? etc.” The data from categorical variables are usually words, often it is simpy “YES, YES, YES, NO, YES, NO” If it was weight, then the data would be quantitative like “125, 155, 223, 178, 222, etc..” The data from quantitative variables are numbers.

73
Q

What does r2 tell us?

r-squared

A

It tells us the percent of variablility of y that is explained by the model with x.

74
Q

If there is a crazy outlier, what can you do?

A

Run the analysis with and without the outlier and write about both.

75
Q

What if the scatterplot is curved?

A

Either straighten the scatterand fit a line,
or keep it and fit a curve
Try quadreg, cubicreg, lnreg, logreg and check the graph and the r.

76
Q

How can you describe shape?

A

TWO THINGS: modes and symmetry.unimodal, bimodal, multimodal AND uniform, symmetric, skewed

77
Q

If the distribution is bimodal or multimodal, what would you use for center and spread statistics?

A

Talk about each mode (center) and maybe use the range or IQR. You could also say “one group seems to go from __ to __ and the other from about __ to __”

78
Q

What’s the difference between a prospective and a retrospective study?

A

A retrospective study takes a group and looks back at its history while a prospective study watches a group for a period of time and records the data along the way into the future.

79
Q

What percent of the data is between Q1 and Q3?

A

the middle 50%. That is the IQR

80
Q

How do you describe distributions (histograms)?

A

Shape-Cener-Spread- and STRANGE (Outliers and gaps) some say GSOCS. where’s yo GSOCS?

81
Q

Gender and Video Game playing are___________ because_______

A

associated (or not independent) because a higher percentage of males play video games. (think.. It depends on gender)

82
Q

What is the median?

A

the middlest number, it splits area in half (always in the POSITION (n+1)/2 )

83
Q

which calculator function gives you a percent?

A

normcdf(Z left, Z right)

84
Q

Computer ouput:

What does “constant” mean?

A

It is the y intercept

85
Q

How do you interpret slope?

A

For an increase of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y].
You can write “SLOPE UNITS Y/ ONE UNITS X” to help

86
Q

How do you find relative frequency?

A

just divide frequency by TOTAL?.

87
Q

First step in interpreting slope

A

Write “slope units y over 1 unit x” and look at it.

88
Q

What is meant by cumulative frequency?

A

ADD up the frequencies as you go. Suppose you are selling 25 pieces of candy. You sell 10 the first hour, 5 the second, 3 the third and 7 in the last hour, the cumulative frequency would be 10, 15, 18, 25

89
Q

Why is it called the”least squares regression line?”

the LSRL?

A

Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distancesto that line from each point.
Itminimizes the squared residuals, the least squares….

90
Q

If asked to compare distributions, what should you write about?

A

A sentence comparing the SHAPES. A sentence comparing the CENTERS. A center comparing the SPREADS. and a sentence comparing the STRANGE STUFF. (GSOCS)

91
Q

Why don’t we always use the mean, we’ve been calculating it all of our life ?

A

It is not RESILIENT, it is impacted by skewness and outliers

92
Q

If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and I do this because I want to know the true average number of pickles on a bur

A

parameter, a one number summary of the population. The truth. AKA the parameter of interest.

93
Q

What does invnorm do?

A

It gives you the Z SCORE from a percentile

94
Q

What is a “percentile?”

A

It tells you the percent of data BELOW a certain value

95
Q

How do you describe CENTER for unimodal and symetric distributions?

A

use the MEAN

96
Q

How do you find Q1 and Q3?

A

Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)

97
Q

Compare data to statistics

A

Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a “statistic” if we have data from each member of population, then that mean is called a “parameter”

98
Q

What symbols do we use for population proportion (%) and sample proportion (%)?

A

p for population and p-hat for sample

99
Q

How do you find a certain percentile on an OGIVE?

A

Start at the % on the Y axis.. travel horizontally to the right until you hit the line, then straight down to the X axis. That data value is the percentile.

100
Q

What does GSOCS stand for?

A

Gaps Shape Outliers Center Spread (put on your gsocs when comparing distributions) be sure to talk about each one clearly (make a list)

101
Q

What if a scatterplot goes straight across horizontally?

A

NO ASSOCIATION.

That would be like height and IQ, they are independent so each height has about the same IQ.

102
Q

Give example of incorrectly using the word “correlation”

A

“there is a correlation between gender and video game playing”
This person should say “association.”
You can’t say correlation because gender is categorical.

103
Q

if you mult or divide the x’s or y’s (shift/scale) does r change?

A

no. the strength remains the same. (If you log or square it, it will change, but just adding or multiplying won’t change it)

104
Q

How do you describe SPREAD for bimodal or multimodal?

A

talk about the outer edges of the clusters “from here to here” or use the IQR.

105
Q

What percentile is the median (aka Q2)?

A

50th

106
Q

not associated is the same as being ____________

A

independent

107
Q

What symbols do we use for population mean and sample mean?

A

Mu for population mean, xbar for sample mean.

108
Q

Diff between association or correlation?

A

association is talking about a relationship.
If you see a pattern in the scatterplot, there is an association.
Correlation is an actual calculated number (two quantitative variables)

109
Q

What is the mean?

A

the old average we used to calculate. It is the balancing point of the histogram

110
Q

What is the mode?

A

the most common, or the peaks of a histogram. We often use mode with categorical data

111
Q

what is a clear example of the medians resiliance and when you would use the median instead of the mean?

A

(change just the top value). Imagine if we asked eight people how much money they had in their wallet. We found they had {1, 2, 2, 5, 5, 8, 8, 9}. The mean of this set is 5, and the median is also 5. You might say “the average person in this group had 5 bucks.” But imagine the same group the next week, but one of them just got back from the casino and the dist was (1, 2, 2, 5, 5, 8, 8, 9000}, in this case, the median would still be 5, but the mean goes up to over 1000. Which number better describes the amount of money the average person in the group this time? 5 bucks or 1000 bucks? I think 5 is a better description of the average person in this group and the 9000 is simply an outlier.

112
Q

Another name for “skewed right” is

A

positively skewed

113
Q

What does r tell us?

A

The direction (+/-) and how strong a LINEAR relationship is between two QUANTITATIVE variables… (when linear)

114
Q

Compare data to parameters

A

Data is each little bit of information collected from the subjects?. They are the INDIVIDUAL little things we collect? we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a “statistic” if we have data from each member of population, then that mean is called a “parameter”

115
Q

Can numbers be CATEGORICAL?

A

sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.

116
Q

Interpret residual: Points above the line/positive resid

A

“the model underpredicted” or “actual performance was above the expected performance

117
Q

How do you descrive SPREAD for unimodal and symmetric distributions?

A

use the standard deviation

118
Q

Can there be a correlation between grade and music preference?

A

No, music preference is categorical.

There is an association, however.

119
Q

Q: How can you get a parameter? A: By taking a ___________

A

Census

120
Q

When we say the average teenager are we talking about mean

A

It depends, if we are talking height, it might be the mean, if we are talking about parental income, we’d probably use the median, if we were talking about music preference, we’d probably use the mode to talk about the average teenager.

121
Q

Which is explanatory variable?

A

the x
the horizontal axis.
it “explains” what happens to y

122
Q

How can you turn OGIVES into histograms?

A

RECTANGLE DROP! (bin drop)

123
Q

Give example of correlation without causation and explain the lurking variable.

A

Ski accidents are higher on days with more hot chocolate sales, therefore, hot chocolate must cause ske accidents. (lurking variable: the number of people on the mountain). What is happening is that on days when the mountain is crowded, there are more hot chocolate sales and more ski accidents. So the population on the mountain is causing both to rise and fall together.

124
Q

If r= 0.8.

An x value that is 2 standard deviations above the mean will have a predicted y value that is _______

A

1.6 standard deviations above the mean in the Y direction

125
Q

Computer Output:

What is “S”

A

The average, or typical residual..
Standard deviation of the residuals
typical distance from actual value to the model’s prediction.
About how far off your prediction is likely to be.

126
Q

What percent of the data is above Q3?

A

25%

127
Q

How can you tell if variables in a contingency table are independent?

A

If the distributions are the same across the variables.. Then it doesn’t DEPEND… so INDEPENDENT. Ex: 30% of freshman and 30% of seniors like cabbage.

128
Q

does correlation mean causation?

A

NO WAY DUDE

129
Q

How can you check for “straight enough?”

A

Residuals plot fool!

check the resids

130
Q

What are the percentiles for Q1, med, and Q3?

A

25, 50 and 75

131
Q

Does the regression line (LSRL) go through a lot of points?

A

No, usually it goes through NONE!

It just goes through the center of the cloud of points.

132
Q

What do you call things that are not independent?

A

associated. Or not independent. We generally don’t say DEPENDENT (unless talking about y variable on a scatterplot).

133
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a cluster sample

A

Imagine that all of art classes have 10 students and they are mixed with fr, so, jr and srs… You would randomly choose 4 classes and survey everyone in each of the 4 classes.

134
Q

What is cluster sampling?

A

Cluster- grab clusters of the population. each cluster should be representative ( like the population) use a few clusters.

135
Q

What is random sampling?

A

When we use chance to select a sample, like rolling dice, a random number generator, or a random number table in our selection process. We use randomization in all of the “GOOD” sampling methods.

136
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a stratified sample

A

Stratify by year. Randomly choose 10 FR, 10 SO, 10 JU and 10 SENIORS

137
Q

What is stratified sampling?

A

When you break the population into groups with similar attributes and randomly select from each strata.

138
Q

What are the “bad” sampling methods.

A

convenience samples and voluntary samples

139
Q

When sampling, what kind of sample are we striving to get?

A

A representative sample, we want our sample to have similar charactaristics as the population

140
Q

What are the “good” sampling methods?

A

SRS (simple random sample), stratified, clustered, systematic, multistage

141
Q

What is systematic sampling?

A

collecting data from every nth subject.

142
Q

What is a simple random sample?

A

put all of the names in a hat. every group is possible. pull the numbers or names

143
Q

A 4 year high school of 2000 students, sampling 40 high students: Describe a convenience sample

A

Ask the first 40 students coming to the locker rooms after school. This is problematic because athletes may not have the same preferences as non athletes.

144
Q

What is a representative sample?

A

A sample that looks like the population. It has similar characteristics.

145
Q

What is the standard sampling method? (the gold standard)

A

A Simple Random Sample (SRS) is our standard. Every possible group of n individuals has an equal chance of being our sample. That’s what makes it simple. Put the names in a hat.

146
Q

A 4 year high school of 2000 students, sampling 40 high students : Describe a systematic sample

A

Get an alphabetical list of all of the students, 2000/40=50. Randomly choose one of the first 50 students and then every 50th student after that.

2020 AP STATISTICS CONCEPT MASTERY (15 decks)

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