Statistics Flashcards
Statistics
The Study of Variability
Variability
How things differ
Ex. Eye Color, Race, Behavioral
Branches of AP STATS
Inferential and Descriptive
Descriptive Stats
Descriptions of the collected data
Inferential Stats
When you take data from a sample and use it to make a inference about a population
Difference between Descriptive and Inferential Stats
Descriptive Stats describes sets of data. Inferential Stats draw conclusions on data based on sampling
Data
Any collected info, each little measurement
Population
The group of interest. Can be big (US population) or small (High School Class)
Sample
A subset of the population. Often taken to make inferences about population. Used to calculate statistics
Comparing Population and Samples
Population contains all members of the specified group. Samples contain part (sample) of the population. Sample size are always smaller than population size.
Compare Data to Statistics
Data is any collected data, each little measurement. Statistics is the numerical summary of the sample of data.
Compare Data to Parameters
Data is the info we collect from the subjects. We the summarize and find the average. If it is a sample, you can call the average found a statistic.
If we have data from each member of the population, the average is called the parameter
Parameter
A numerical summary of a population. Mean, Median
Mode ect of population.
Statistic
A numerical summary of a sample. Mean, Median,
Mode, ect of a sample.
You wanted to find the average wait time at a Dunkin drive through in your neighborhood. You randomly sampled cars and found 3.2 minute average wait time. What is population parameter? What is the statistic? What is the parameter of interest? What is the data?
Population Parameter: True average wait time at that Dunkin.
Statistic: 3.2 minutes. Average of the data collected
Parameter of Interest: True average wait time of all cars
Data: Wait time of each individual car. Data taken by each car used to find average, which is called a statistic. You then make an inference of the true parameter
Compare Data/ Statistic/ Parameter using categorical example
Data: Individual measures like meal preference/ hair color ect.
Statistic/Parameter: Summaries. Statistic would be 42% of
SAMPLE preferred tacos
Parameter would be 42% of POPULATION preferred tacos.
Compare Data/ Statistic/ Parameter using quantitative example
Data: Individual measures like how long can a person be underwater. 10 sec, 15 sec, 20 sec is raw data.
Statistic: Summary of data. Average time underwater in the SAMPLE was 10.3 seconds
Parameter: Summary of data. Average time underwater in the POPULATION was 10.3 seconds
Census
When information is gathered from every member of the population
Does a Census make sense?
It is ok for small populations (surveying a high school class) but impossible if you wanted to survey all US teens
Difference between a Parameter and a Statistic
Parameters come from populations while Statistics come from samples
Random sample from 20 burgers at FG and counted the pickles on them and one of the burgers has 9 pickles, the 9 from that burger is the___
Datum or data value
Random sample from 20 burgers at FG and counted the pickles on them and the average number of pickles was 9.5, then 9.5 is considered a ____
Statistic
Random sample from 20 burgers at FG and counted the pickles on them and I do this to find the true average number of pickles at FG, the true average number of pickles is considered a ____
Parameter
Difference between Sample and a Census
In a sample, you get info from a small part of a population. In a census, you get info from the entire population. You get statistic form a sample, and a parameter from a census
Use these words in a sentence. Population, Parameter, Census, Sample, Data, Statistics, inference, and Population of Inference
I was curious about a population parameter but the census was unreasonable so I decided to take a sample, collect some data, calculate the statistic and use it to make an inference about the population parameter.
If you are tasting soup, flavor of the individual thing in the spoon is the 1. The entire spoon is the 2. Flavor of all of the stuff together is like the 3 and you use that to 4 about the flavor of the entire pot of soup, which would be the 5
1=Data 2=Sample 3=Statistic 4=Make an Inference 5=Parameter
Random Variables
Data collected from a random sample. Ex. If you gathered a group of random kids, eye color, hair color, skin color, size, age or all random variables
Difference between Quantitative and Categorical variables
Quantitative variable are numeric. Categorical variables are categories like hair color, skin color ect.
Difference between Quantitative and Categorical Data
Quantitative Data is just numbers. Categorical data is the actual category gathered for each subject.
Difference between Discrete and Continuous Variables
Discrete data can only take certain values. Ex. Counting the number of students a classroom, you can’t have 1/2 of a student. Have more simple numbers
Continuous Variables can take whatever value like a race car race, which can be fractions of a second. More complex numbers
Quantitative Variable
Are numeric like height, age, weight
Categorical Variable
Are like categories. Eye Color, Hair color, Music Styles, Gender
What do we sometimes call a Categorical Variable?
a Qualitative Variable
Quantitative Data
Actual numbers gathered from each subject.
Ex. 213 pounds, 17 inches
Categorical Data
The actual category for each subject
Ex. Female, Grade
Random Sample
When a sample is chosen 100% randomly
Ex. Cards, Dice
Frequency
How often something comes up
Datum vs Data
Datum=Singular Version
Ex. Come look at this datum from this dog
Data=Plural version
Ex. Come look at this dat from the dogs.
Frequency Distribution
A chart showing how often certain values occur in a data set
Relative Frequency
The percent of time something comes up.
frequency/total
Formula for Relative Frequency
Divide the frequency by the total
Cumulative Frequency
The frequencies added up as you go
Ex.10, 15, 20
10, 25, 45
Relative Cumulative Frequency
It is the added up cumulative frequencies, but in a percentage. You then divide it by the total
Bar Chart vs Histogram
Bar Charts plot categorical data and bars don’t touch. Histograms plot quantitative data and bars touch.
Mean
It is the average of numbers. It is the balancing point of a histogram
Population Mean vs Sample Mean
Population mean is the mean of a population, it is the perameter. Sample mean is the mean of a sample, so it is a statistic. Sample statistics are used to make inferences about population perameters.
Symbols of Population Mean and Sample Mean
Population Mean= μ (mu)
Sample Mean= x̄ (x bar)
How to think about Mean and Median when looking at a histogram
Mean= balancing point of histogram Median= Splits area of histogram in half
Median
The Middle number of a set of numbers. It splits area in half
Mode
Value that appears most often in a list of numbers.
When do we often use Mode?
With categorical variables. For ex calculating music preference, you say how “most student prefer _ which is the mode.
Why don’t we always use the Mean?
It is impacted by outliers and skewness. It is not resilient.
When you say “the average teenager” are you talking about the mean, median or mode?
It depends.
Mean= Could be used the calculate height preference
Median= Could be used to calculate parental income
Mode= Could be used to calculate music preference
Example of the mean would change but median wouldn’t
If you asked a group of people how much they had in their wallet and found they had (1,2,2,5,5,8,8,9). Mean would be 5 and the median would also be 5. Imagine however if they just came back from the casino and had (1,2,2,5,5,8,8,9000). Median would still be 5 but the mean would change to over 1,000 because of the outlier. The number $5(median) or $1,000 (mean) carried by the average person is best described by the median.
How are mean, median and mode positioned in a skewed left histogram?
In order from left to right, mean-median-mode
How are mean, median, mode positioned in a skewed right histogram.
Opposite, mode-median-mean
Who chases the tail?
The mean chases the tail, the mean chases the tail…
Way to study efficiently instead of rereading the vocab
Go to APSTATSGUY and click on Summer Vocab link. Open account on Brainscape and create deck. Rate the cards honestly.
