Summer Vocab Flashcards
Statistics
Study of variability
population
group of interest, can be big or small
Variability
All things have differences, and statisticians look a these differences
2 branchs of AP stats
inferential and descriptive
descriptive stats
describe collected data using pictures or summaries like mean, median, range, etc…
inferential stats
look at data of sample and use it to tell about the population
compare descriptive and inferential stats
descriptive explains about data; inferential uses data of sample to tell about an entire population
data
any collected info., generally each little measurement
sample
A subset of population, taken to make inferences about the population, calculate statistics from samples
compare population to sample
populations generally are large, samples are small subsets of population; take samples to make inferences about populations, use statistics to estimate parameters
compare data to statistics
data is the individual bits of info collected, summarize data by, ex. finding mean of a group of data,
mean of sample is statistic, if data is from each member of population, mean is parameter
compare data to parameters
data is the individual bits of collected info, summarize data by, ex. finding mean of a group of data,
mean of sample is statistic, summary of sample; if data is from each member of population, mean is parameter, summary of population
parameter
numerical summary of a population like mean, median, mode
statistic
numerical summary of a sample like mean, median, mode
Curious about average wait a Dunkin Donuts drive through: randomly sample cars and find the average wait time is 3.2 minutes. What is the population parameter, statistic, parameter of interest, data?
parameter is the true average wait time at that Dunkin Donuts, a number you don’t have and will never know. Statistic is 3.2 minutes, average of data collected. Parameter of interest= population parameter. Data is the wait time of each individual car, like “3.8 min, 2.2 min, 0.8 min.” Average of that data is statistic, and use that to make inference about the true parameter
Compare DATA-STATISTICPARAMETER using categorical
example
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.”
Compare DATA-STATISTICPARAMETER using quantitative
example
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”
What is a census?
Like a sample of the entire population, you get information from every member of
the population
Does a census make sense?
A census is ok for small populations (like Mr. Nystrom’s students) but impossible if
you want to survey “all US teens”
What is the difference between a
parameter and a statistic?
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS….
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 datum, or a data value.
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
statistic. (t is a summary of a sample.)
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
parameter, a one number summary of the population. The truth. AKA the
parameter of interest.
What is the difference between a
sample and a census?
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.
Use the following words in one
sentence: population, parameter,
census, sample, data, statistics,
inference, population of interest
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).
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\_\_\_\_\_\_\_\_\_\_.
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.
What are random variables?
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.
What is the difference between
quantitative and categorical
variables?
Quantitative variables are numerical measures, like height and IQ. Categorical are
categories, like eye color and music preference
What is the difference between
quantitative and categorical data?
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.
What is the difference between
discrete and continuous variables?
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.
What is a quantitative variable?
Quantitative variables are numeric like: Height, age, number of cars sold, SAT
score
What is a categorical variable?
Qualitative variables are like categories: Blonde, Listens to Hip Hop, Female, yes,
no… etc.
What do we sometimes call a
categorical variable?
qualitative
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per
minute.
What is categorical data?
The actual individual category from a subject, like “blue” or “female” or
“sophomore”
What is a random sample?
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
What is frequency?
How often something comes up
data or datum?
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!!”
What is a frequency distribution?
A table, or a chart, that shows how often certain values or categories occur in a
data set
What is meant by relative
frequency?
The PERCENT of time something comes up (frequency/total)
How do you find relative frequency?
just divide frequency by TOTAL….
What is meant by cumulative
frequency?
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
Make a guess as to what relative
cumulative frequency is…
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.
What is the difference between a
bar chart and a histogram
bar charts are for categorical data (bars don't touch) and histograms are for quantitative data (bars touch)
What is the mean?
the old average we used to calculate. It is the balancing point of the histogram
What is the difference between a
population mean and a sample
mean?
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.
What symbols do we use for
population mean and sample mean?
Mu for population mean (parameter), x-bar ̅ for sample mean (statistic)
How can you think about the mean
and median to remember the
difference when looking at a
histogram?
mean is balancing point of histogram, median splits the area of the histogram in
half.
What is the median?
the middlest number, it splits area in half (always in the POSITION (n+1)/2 )
What is the mode?
the most common, or the peaks of a histogram. We often use mode with
categorical data
When do we often use mode?
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…).
Why don’t we always use the mean,
we’ve been calculating it all of our
life ?
It is not RESILIENT, it is impacted by skewness and outliers
When we say “the average
teenager” are we talking about
mean, median or mode?
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.
what is a clear example of where the
mean would change but median
wouldn’t? (this would show its
resilience)
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.
How are mean, median and mode
positioned in a skewed left
histogram?
goes in that order from left to right. Mean-median-mode
How are mean, median and mode
positioned in a skewed right
histogram?
goes in the opposite order.. Mode-median-mean
Who chases the tail?
The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean
chases the tail… and outliers…….
Is there a way to study these
efficiently instead of just rereading
them?
YES.. Go to APSTATSGUY.COM and click on the SUMMER VOCAB FLASHCARDS link.
Make sure to open account at BRAINSCAPE.COM and then add this deck to your
library. Follow the directions. RATE THE CARDS HONESTLY FOR SUPER RESULTS!!
