AP Statistics Summer Vocabulary Flashcards
What is Statistics?
The study of variability
What is variability?
Differences… how things differ. THere is variability everywhere.. We all look different, act different, have different preferences… Statisticians look at these differences.
What are 2 branches of AP STATS?
Inferential and Descriptive
What are Descriptive Stats?
Tell what you got , describe data you collected use pictures or summaries like mean, median, range
What are inferential Stats?
Look at data and use it to say stuff about the big picture. little sample can tell a lot about the whole population
Compare Descriptive and Inferential Stats
Descriptive explains about data you have,, inferential uses data to try to say something about an entire population
What is data?
Any collected information. generally each little measurement
What is a population?
the group you’re interested in. can be big or small
What is a sample?
a subset of a population, often taken to make inferences about the population. we calculate statistics from sample
compare population to sample
populations are generally large, and samples are small subsets of these populations. samples are used to make inferences from populations and statistics are used to estimate parameters
Compare data to statistics
data is each little bit of information collected from the subjects and are individual things collected we can summarize by ex. finding mean of a group of data. If it is a sample we call that mean a “statistic” and if we have data from each member of population its a “parameter”
compare data to parmeters
data is each little bit of information collected from the subjects and are individual things collected we can summarize by ex. finding mean of a group of data. If it is a sample we call that mean a “statistic” and if we have data from each member of population its a “parameter”
what is a parameter?
a numerical summary of a population. ex. mean, median range of a population
what is a statistic?
a numerical summary of a sample. like mean median range of a sample
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?
The parameter is the true average wait time at the 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.
Compare Data-statistic-parameter using categorical example
Data are individual measures, like meal preferences “taco, taco pasta, etc.” Statistics and parameters are summaries. a statistic would be “42% of sample prefer tacos” and a parameter would be “42% of population preferred tacos.”
Compare data-statistic-parameter 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. Nystom’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 numbers summarizing a larger group of numbers but pppp parameters come from pppp populations sss statistics come from ssss statistics
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 has 9 pickles, then the number 99 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 (summary of a sample)
If I take a random sample 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 on sentence: population, parameter, sensus, sample, data, statistics, interference,, 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 interference 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
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’s eye color, then the data would look like this “blue, brown, brown, brown, blue, green,.. etc.” The data from categorical variables are usually words, often it is simply “YES, YES, NO, YES” If it was weight, then the data would be quantitative like “125, 155, 223, 222, etc…” The data from quantitative variables are numbers.
What is the difference between discrete and continuous data?
Discrete can be counted, like “number of cars” they are generally integers (no decimal of a car) while continuous would be something like the weight of a mouse.. 4.344 oz.
What is 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
What is categorical data?
The actual individual category from each subject, like “sophomore” or “female”
What is a random sample?
When you choose a sample by rolling dice, choosing names from a hat or or another 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. (ex. datum from one rat) data is plural (data from several chimpmunks)
What is a frequency distribution?
a table, 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 the frequency by the total
What is meant by cumulative frequency?
ADD up the frequencies as you go.
What is relative cumulative frequency
The ADDED up PERCENTAGES. 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 (μ) for population mean (parameter), x bar (x̄) 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 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 describes 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 of our life?
It is not RESILIENT. it is impacted by skewness and outliers
When we say the “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 when 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 describes the amount of money the average person in the group carries, 5 bucks or 1000 bucks? 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
