Beginning AP Stats Vocab Flashcards
What is statistics?
The study of variability
What is variability?
Differences (how things differ). Examples include differences in looks, behaviors, and preferences—all of which are studied by statisticians.
What are the two branches of AP Stats?
Inferential and Descriptive
What are DESCRIPTIVE stats?
Stats used to describe data using pictures and summaries like mean, median, and mode; facts
What are INFERENTIAL stats?
Stats used to generalize data (like how one sample describes the rest of the population); predictions
Compare DESCRIPTIVE and INFERENTIAL stats
Descriptive describes the data set you have, and inferential uses data to say something about the greater population
What is data?
Any collected information (each little measurement, generally)
What is a population?
A group from which data is collected
What is a sample?
A subset of a population taken to make inferences about the population in general. Statistics are calculated from samples
Compare population to sample
Populations are usually large, and samples are small subsets of populations. We take samples to make inferences about populations. We use statistics to estimate parameters.
Compare data to statistics
Data is every little bit of information collected from subjects within a population that are summarized in different ways (such as finding the mean in a group of data). If it is a sample, then the mean is called a “statistic”; if we have data from each member of a population, then the mean is called a “parameter”
Compare data to parameters
Data is every little bit of information collected from subjects within a population that are summarized in different ways (such as finding the mean in a group of data). If the data is from a sample, then the mean is called a “statistic”; if we have data from each member of a population, then the mean is called a “parameter”
What is a parameter?
A numerical summary of a population. The mean, median, mode, and range of a population are considered parameters
What is a statistic?
A numerical summary of a sample. The mean, median, mode, and range of a sample are considered statistics
We are curious about the average wait time at Dunkin’ Donuts drive-thru in your neighborhood. You randomly sample cars one afternoon and find the average wait time is 3.2 minutes. What is the parameter? What is the statistic? What is the parameter of interest? What is the data?
The parameter is the true average wait time at 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 from the random sample. The parameter of interest is the same 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, such as “3.8 min 2.2 min, .8 min, 3 min.” You take that data and find the average, that average is called the “statistic,” and you use that to make an inference about the true parameter.
Compare data, parameter, and statistic using a categorical example
Data are individual measures, like meal preference (taco, taco, burger, pizza, burger, taco, pizza), parameters and statistics are summaries. A statistic could be “42% of the sample prefer tacos” and a parameter could be “42% of the population prefer tacos”
Compare data, parameter, and statistic using a quantitative example
Data are individual measures, like how long a person can hold their breath (45 sec, 22 sec, 52 sec, 48 sec). That is the raw data. Statistics and parameters are summaries of the data; a sample could be “the average breath holding time in the sample was 52.4 seconds,” and a parameter could be “the average breath holding time in the population was 52.4 seconds”
What is a census?
Like a sample of the entire population, but you get information from EVERY member of the population
Does a census make sense?
A census is okay for small populations (like a classroom of students), but it is impossible if you want to survey “all U.S. teens”
What is the difference between a parameter and a statistic?
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGE GROUP OF NUMBERS…. but parameters come from POPULATIONS (think P for pop.), and statistics come from SAMPLES (think S for samp.)
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 a _____.
“datum,” or a data value
If I take a random sample of 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 the ______.
statistic (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 the _____.
parameter (a summary of a 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 group within a population, and with a census, you get information from the entire population. You can determine 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 _____.
data, sample, statistic, make an inference, parameter. Notice you are interested in the parameter to begin with… that is why you took the 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 variables are categories, like eye color and music preference.
What is the difference between quantitative and categorical data?
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, brown, etc.” The data from categorical variables are usually WORDS, often it is simply “yes, yes, no, yes, no.” If it was weight, then the data would be quantitative like “123 lbs, 243 lbs, 194 lbs, 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 (whole numbers), while continuous would be something like the weight of a mouse “4.344 oz”; these may not be whole numbers
What is a quantitative variable?
(Quantitative) numeric variables like height, age, number of cars sold, SAT scores
What is a categorical variable?
(Qualitative) categorical variables like 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 lbs, 67 bpm, 80 mph
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 another 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 plural, like “hey, look at all that data Edgar got from those chipmunks over there!”
What is frequency distribution?
A table or 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?
divide frequency by total
What is meant by cumulative frequency?
ADD up the frequencies as you go. Suppose you are selling candy, 25 pieces sold overall… with 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 cumulative relative frequency is…
It is the ADDED UP PERCENTAGES. Like for the selling candy example: 10 the first hour, 5 the second, 3 the third and 7 in the last hour, we’d take the cumulative frequencies 10, 15, 18, 25 and divide by the total (25) giving cumulative percentages (.40, .60, .64, 1.00). Relative cumulative frequencies ALWAYS end up at 100 percent
What is the difference between a bar chart and a histogram?
Bar charts are for categorical data (the bars don’t touch), and histograms are for quantitative data (the bars touch)
What is the mean?
The old average we used to calculate; 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 and is a parameter. Sample mean is the mean of a sample and 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 (μ) for population mean (parameter), and x-bar (x̅) for sample mean (statistic)
How can you think about the mean and median to remember the difference when looking at a histogram?
Mean is the balancing point of the histogram, and the median splits the the area of the histogram in half
What is the median?
The middlest number, it splits the area in half (always in the POSITION (n+1)/2)
What is the mode?
The most common, or peaks of a histogram. We often use mode in 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 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 our lives?
Because it is not RESILIENT, it is impacted by skewness and outliers
When we say “the average teenager,” are we talking about the mean, median, or mode?
It depends: if we are talking about height, it might be the mean; if we are talking about parental income, we would probably use the median; if we are talking about music preference, we would probably use the mode
What is a clear example of where the mean would change but the median wouldn’t? (this would show its resilience)
Imagine if we asked 8 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 has five dollars,” but imagine if one of them just got back from the casino, and instead it was {1, 2, 2, 5, 5, 8, 8, 9,000}. In this case, the median would still be 5, but the mean goes up to over 1,000. Which number better describes the amount of money the average person in the group carries, 5 bucks or 1000 bucks? 5 is the better description of the average person in this group and 9,000 is simply the outlier.
How are mean, median, and mode positioned in a skewed left histogram?
They go in that order from left to right (mean, median, mode)
How are mean, median, and mode positioned in a skewed right histogram?
They go in the opposite order (mode, median, mean)
Who chases the tail?
The MEAN chases the tail (and outliers)
