Summer Vocab Flashcards
The study of variability
Statistics
Differences… how things differ. We all look different, act differently, have different preferences…
Variability
2 branches of AP Stats
Inferential and Descriptive
Describe data collected, pictures, or summaries like mean, median, and mode.
Descriptive Stats
Look at data and use that to say stuff about the big picture (little sample can tell a lot)
Inferential Stats
___ explains to you about the data you have while ___ uses that data you have to try to say something about an entire population
Descriptive vs. Inferential Stats
Any collected information. Generally each little measurement.
ex. ¨yes, yes, no, yes, yes¨ or ¨3, 1, 2, 1, 4, 3, 3, 4¨
Data
Group you’re interested in
ex. “all teenagers in the US” or “all AP students in my school
Population
A subset of a population, often to make inferences about the population. Used to calculate stats
Sample
___ are generally large
___ are smaller subsets of this ___
Population vs. Sample
___ is each little bit of info collected from the subjects, INDIVIDUAL, summarized (ex. finding the mean of group of data aka statistic)
If there’s data from each member of pop. called a ___
Data vs. Statistics vs. Parameters
A numerical summary of a population
ex. mean, median, range of a sample
Parameter
A numerical summary of a sample
ex. mean, median, range of a sample
Statistic
___ are individual measures. ex. meal preferences “taco, taco, pasta, burger, burger, taco”
___ and ___ are summaries. ex. stat “42% of sample preferred tacos” and parameter “42% of population preferred tacos”
Data vs. Statistic vs. Parameter (Categorical)
Individual measures, ex. how long a person can hold their breath “45s, 64s, 32s, 68s” = raw data
Summaries, ex. “ the average breath holding time in the sample was 52.4s” and “the average breath holding time in the pop. was 52.4s”
Data vs. Stat vs. Parameter (Quantitative)
Like a sample of the entire population, get info from every member of pop.
Census
A census is okay for small populations, ex. a classroom
bad for “all US teens”
Does a census make sense?
Both are single number summarizing a larger group of numbers.
ex. pppp parameters come from pppp pop. and ssss stats come from ssss stats
Parameter vs. Statistic
a value in a data set
ex. # of pickles on a burger
Datum (data value)
ex. average # of pickles on a bunch of burgers
Statistic (summary of a sample)
ex. true average # of pickles on a burger
Parameter (1 # summary of the population)
In a ___, you get info from a small part of the population.
In a ___, you get info from the entire population
You can get a parameter from a census, but only a statistic from a sample
Sample vs. Census
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 are random variables?
___ are numerical measures, ex. height and IQ
___ are categories, ex. eye color and musical preference
Quantitative vs. Categorical Variables
The data is the actual gathered measurements.
ex. eye color “blue, brown, brown, etc.” or “yes, no”
ex. weight “125, 155, 223, 178, etc.”
Quantitative vs. Categorical Data
___ is a finite number of values between any two values. It’s always numeric.
ex. # of cars sold (24)
___ is an infinite number of values between any two values. It can be numeric or date/time.
ex. weight of a mouse (4.344 oz)
Discrete vs. Continuous Variables
Numeric
ex. Height, age, SAT score
Quantitative Variable
Categories
ex. Blonde, Listens to Hip Hop, Female, yes, no, etc.
Categorical Variable
What do we sometimes call a categorical variable?
Qualitative
The actual #’s gathered from each subject.
ex. 211 lbs, 67bpm
Quantitative Data
The actual individual category from a subject
ex. blue, female, sophomore
Categorical Data
Real randomly generated sample
Humans can’t really do this well without the help of a calculator, cards, dice, or slips of paper
ex. rolling dice, choosing names from a hat, etc.
Random Sample
How often something comes up
Frequency
___ is singular
ex. “hey dude, come see this datum I got from this rat!”
___ is the plural
ex. “hey look at all that data Edgar got from those chipmunks over there!!”
Data or Datum?
A table, or a chart, that shows how often certain values or categories occur in a data set
Frequency Distribution
Divide frequency by total
Relative Frequency
Add up frequencies as you go.
Suppose you’re selling 25 pieces of candy. You sell 10 the first hour, 5 the second, 3 the third, and 7 in the last.
ex. 10, 15 18, 25
Cumulative Frequency
It is the added up percentages.
Take cumulative frequencies and divide by total.
Always end at 100 percent.
ex. .40, .60, .64, .1.00.
Relative Cumulative Frequency
___ are for categorical data (bars don’t touch)
___ are for quantitative data (bars touch)
Bar Chart vs. Histogram
The old average we used to calculate. It is the balancing point of the histogram.
Mean
___ mean is the mean of a population
ex. parameter
___ mean is the mean of a sample
ex. statistic
We can use sample stats to make inferences about population parameters.
Population Mean vs. Sample Mean
Symbols used for pop. mean (μ) and sample mean (x̅)
Mu and x bar
Mean is the balancing point of a histogram, median splits the area of the histogram in half.
How can you think about the mean and median to remember the difference when looking at a histogram?
The middlest #, it splits the area of a histogram in half
Median
The most common, or the peak of a histogram. We often mode with categorical data.
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…).
When do we often use mode?
It is not RESILIENT, it is impacted by skewness and outliers
Why don’t we always use the mean?
It depends
mean= height
median= parental income,
mode= music preference
When we say “the average teenager” are we talking about mean, median or mode?
Goes in that order from left to right. Mean-median-mode
How are mean, median, and mode positioned in a skewed left histogram?
Goes in opposite order from right to left. Mode-median-mean
How are mean, median, and mode positioned in a skewed right histogram?
The mean chases the tail
The mean chases the tail
