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Summer study > AP STATS Summer homework > Flashcards

AP STATS Summer homework Flashcards

1
Q

What is Statistics?

A

The study of variability

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2
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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3
Q

What are 2 branches of AP STATS?

A

Inferential and Descriptive

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4
Q

What are DESCRIPTIVE STATS?

A

Tell me what you got! Describe to me the data that you collected, use pictures or
summaries like mean, median, range, etc

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5
Q

What are INFERENTIAL STATS?

A

Look at your data, and use that to say stuff about the BIG PICTURE… like tasting
soup… a little sample can tell you a lot about the big pot of soup (the population)

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6
Q

Compare Descriptive and Inferential

STATS

A

Descriptive explains you about the data that you have, inference uses that data
you have to try to say something about an entire population….

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7
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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8
Q

What is a population?

A

the group you’re interested in. Sometimes it’s big, like “all teenagers in the US”
other times it is small, like “all AP Stats students in my school”

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9
Q

What is a sample?

A

A subset of a population, often taken to make inferences about the population.
We calculate statistics from samples.

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10
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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11
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

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12
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

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13
Q

What is a parameter?

A

A numerical summary of a population. Like a mean, median, range… of a
population

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14
Q

What is a statistic?

A

A numerical summary of a sample. Like a mean, median, range… of a sample

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15
Q 
We are curious about the average
wait time at a Dunkin Donuts drive
through in your neighborhood. You
randomly sample cars one afternoon
and find the average wait time is 3.2
minutes. What is the population
parameter? What is the statistic?
What is the parameter of interest?
What is the data?
A

The parameter is the true average wait time at that Dunkin Donuts. This is a
number you don’t have and will never know. The statistic is “3.2 minutes.” It is the
average of the data you collected. The parameter of interest is the same thing as
the population parameter. In this case, it is the true average wait time of all cars.
The data is the wait time of each individual car, so that would be like “3.8 min, 2.2
min, .8 min, 3 min”. You take that data and find the average, that average is called
a “statistic,” and you use that to make an inference about the true parameter.

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16
Q

Compare DATA-STATISTICPARAMETER 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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17
Q

Compare DATA-STATISTICPARAMETER 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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18
Q

What is a census?

A

Like a sample of the entire population, you get information from every member of
the population

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19
Q

Does a census make sense?

A

A census is ok for small populations (like Mr. Nystrom’s students) but impossible if
you want to survey “all US teens”

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20
Q

What is the difference between a

parameter and a statistic?

A

BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS….
But pppp parameters come from pppp populations… sss statistics come from ssss
statistics.

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21
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 called
\_\_\_\_?
A

a datum, or a data value.

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22
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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23
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
burger at FIVE GUYS, the true
average number of pickles is
considered a \_\_\_\_\_\_?
A

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

24
Q

What is the difference between a

sample and a census?

A

With a sample, you get information from a small part of the population. In a
census, you get info from the entire population. You can get a parameter from a
census, but only a statistic from a sample

25
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)

26
Q 
If you are tasting soup.. Then the
flavor of each individual thing in the
spoon is the \_\_\_\_\_\_\_\_, the entire
spoon is a \_\_\_\_\_\_.. The flavor of all
of that stuff together is like the
\_\_\_\_\_ and you use that to
\_\_\_\_\_\_\_\_\_\_ about the flavor of the
entire pot of soup, which would be
the\_\_\_\_\_\_\_\_\_\_.
A

If you are tasting soup. Then the flavor of each individual thing in the spoon is
DATA, the entire spoon is a SAMPLE. The flavor of all of that stuff together is like
the STATISTIC, and you use that to MAKE AN INFERENCE about the flavor of the
entire pot of soup, which would be the PARAMETER. Notice you are interested in
the parameter to begin with… that is why you took a sample.

27
Q

What are random variables?

A

If you randomly choose people from a list, then their hair color, height, weight and
any other data collected from them can be considered random variables.

28
Q

What is the difference between
quantitative and categorical
variables?

A

Quantitative variables are numerical measures, like height and IQ. Categorical are
categories, like eye color and music preference

29
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.

30
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.

31
Q

What is a quantitative variable?

A

Quantitative variables are numeric like: Height, age, number of cars sold, SAT
score

32
Q

What is a categorical variable?

A

Qualitative variables are like categories: Blonde, Listens to Hip Hop, Female, yes,
no… etc.

33
Q

What do we sometimes call a

categorical variable?

A

qualitative

34
Q

What is quantitative data?

A

The actual numbers gathered from each subject. 211 pounds. 67 beats per
minute

35
Q

What is categorical data?

A

The actual individual category from a subject, like “blue” or “female” or
“sophomore”

36
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.

37
Q

What is frequency?

A

How often something comes up

38
Q

data or datum?

A

datum is singular.. Like “hey dude, come see this datum I got from this rat!” data
is the plural.. “hey look at all that data Edgar got from those chipmunks over
there!!”

39
Q

What is a frequency distribution?

A

A table, or a chart, that shows how often certain values or categories occur in a
data set.

40
Q

What is meant by relative

frequency?

A

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

41
Q

How do you find relative frequency?

A

just divide frequency by TOTAL….

42
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

43
Q

Make a guess as to what relative

cumulative frequency is…

A

It is the ADDED up PERCENTAGES.. An example is selling candy, 25 pieces sold
overall…, with 10 the first hour, 5 the second, 3 the third, and 7 the fourth hour,
we’d take the cumulative frequencies, 10, 15, 18 and 25 and divide by the total
giving cumulative percentages… .40, .60, .64, and 1.00. Relative cumulative
frequencies always end at 100 percent.

44
Q

What is the difference between a

bar chart and a histogram?

A 
bar charts are for categorical data (bars don't touch) and histograms are for
quantitative data (bars touch)
45
Q

What is the mean?

A

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

46
Q

What is the difference between a
population mean and a sample
mean?

A

population mean is the mean of a population, it is a parameter, sample mean is a
mean of a sample, so it is a statistic. We use sample statistics to make inferences
about population parameters.

47
Q

What symbols do we use for

population mean and sample mean?

A

Mu for population mean (parameter), x-bar ̅ for sample mean (statistic)

48
Q

How can you think about the mean
and median to remember the
difference when looking at a
histogram?

A

mean is balancing point of histogram, median splits the area of the histogram in
half.

49
Q

What is the median?

A

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

50
Q

What is the mode?

A

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

51
Q

When do we often use mode?

A

With categorical variables. For instance, to describe the average teenagers
preference, we often speak of what “most” students chose, which is the mode. It
is also tells the number of bumps in a histogram for quantitative data (unimodal,
bimodal, etc…)

52
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

53
Q

When we say “the average
teenager” are we talking about
mean, median or mode?

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.

54
Q

what is a clear example of where the
mean would change but median
wouldn’t? (this would show its
resilience)

A

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
if one of them just got back from the casino, and instead it 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 carries, 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.

55
Q

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

A

goes in that order from left to right. Mean-median-mode

56
Q

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

A

goes in the opposite order.. Mode-median-mean

57
Q

Who chases the tail?

A

The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean
chases the tail… and outliers……

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