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 the two branches of AP Stats
Inferential and descriptive
What are descriptive stats
Describe what you see using pictures or summaries
What are inferential stats
Use your data to make a statement about the big picture
Descriptive vs inferential
Descriptive describes the data you have inferential uses that data to make a statement
What is data
The information collected from each individual
What is a population
The group you are interested in
What is a sample
A subset or small collection of your population
What is a census
When you literally collect data from every individual in your population
What is a parameter
A summary of your populations data
What is a statistic
A summary of your sample
Compare data to statistics
Data is each little bit of information collected from the subjects…. They are the INDIVIDUAL little things we collect… we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a “statistic” if we have data from each member of population, then that mean is called a “parameter”
Compare data to parameters
Data is each little bit of information collected from the subjects…. They are the INDIVIDUAL little things we collect… we summarize them by, for example, finding the mean of a group of data. If it is a sample, then we call that mean a “statistic” if we have data from each member of population, then that mean is called a parameter
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 that 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 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 using quantitative summaries like “the average breath holding time in the sample was 52.4 seconds” example and a parameter would be “the average breath holding time in the population was 52.4 seconds”
Parameter vs. Statistics
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS…. But pppp parameters come from pppp populations… sss statistics come from ssss statistics.
Sample vs. 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 categorical and quantitative/categorical variables?
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) but can not always (shoe size is discrete but you have 9, 9 ½ ,10, 10 ½ ,etc), while continuous would be something like weight of a mouse… 4.344 oz.
What is a quantitative variable?
Can be measured numerically (height, SAT score, GPA, etc)
What is a qualitative/categorical variable?
When data is measured by a category (hair color, listens to hip hop, ethnicity, gender, etc)
What is quantitative data?
The actual numbers gathered from each subject or unit (ex. 200 lbs, 3.6 GPA, 1240 SAT score, etc)
What is categorical data?
The actual category from a subject (ex. Blonde, male, listens to jazz, freshman, etc)
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 or occurs
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
What is relative frequency?
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 symbol do we use for population mean?
Mu
What symbol do we use for sample mean?
x-bar (lowercase x, not capital)
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 mode?
The most common data value or category, the peak of a histogram
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?
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
What chases the tail in histogram?
The mean chases the tail
