SUMMER DECK 1 Flashcards
What is statistics (Nystrom’s def)?
The study of variability
What is variability?
Differencesho… w things differ. There is variability everywhere.. We all look different, have different preferences.. Etc.
What is Statistics (textbook)
The science of collecting, organizing, summarizing, analyzing, and making inferences from data.
What are the 2 major branches of statistics we will study this year?
Inferential and Descriptive
What are DESCRIPTIVE STATS?
Numbers and pictures that describe nature of a data set, provide info about data that is present
What are INFERENTIAL STATS?
Making inferences.. saying what is actually going on in the population, making predictions, using statistics to estimate parameters
Compare descriptive to inferential
Descriptive seeks to tell you about what is in the data at hand, inference looks at a part of the population to tell you what is happening .. (like tasting soup to see if it’s good)
What is data?
Any collected information. Generally each little measurement..
What is a population?
the group you’re interested in. Sometimes it’s big, like “all teenagers in the US” other times it is small like “Mr. Nystrom’s fifth period class.” You calculate parameters from populations.
Compare population to sample
populations are generally large and samples are small subsets of these population. We take samples to make an inference about what we think is true in the population. We use statistics to estimate parameters.
What is a parameter?
A numerical summary of a population. Like a mean, median, range of a population
What is a statistic?
A numerical summary of a sample. Like a mean, median, range of a sample.
What is a sample?
A subset of a population, often taken to make inferences about the population. We calculate statistics from samples
Compare DATA-STATISTIC-PARAMETER using categorical example
Data are individual measures like meal preference:
taco, taco, pasta, taco, burger, burger, taco.
Statistics and Parameters are summaries. A statistic would be 42% of sample preferred tacos and a parameter would be 46% of population preferred tacos.
Compare DATA-STATISTIC-PARAMETER using quantitative example
Data are individual measures, like how long a person can hold their breath: 5 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 52.7 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. Nystrom’s third period class) but not a good idea when the population is “all US teens”. In that case, a census would be expensive, time consuming, and impossible. But if you are ordering pizza for five people, you won’t randomly ask two of them and base your order on that sample. Five is small enough to take a census and get a good order that will make all happy. Yum
What is the difference between a parameter and a statistic?
pppp parameters come from pppp populations? sss statistics come from ssss samples
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
What are random variables?
Variables whose values are determined by chance like, if you randomly choose a student, his hair color is a random variable, so is his height and weight and the diameter of his eyeball and whether or not he likes scones.
What is the difference between quantitative and qualitative (categorical)?
Quantitative are numerical measures, like height and IQ. Qualitative (categorical) are qualities, or categories, like eye color, left-right handedness. The raw data gives a hint. Categorical: red, red, blue, blue, green. Quantitative: 4, 5.3, 7, 8.8 WARNING: Zip codes are categorical and so are jersey 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 9.283 cars), while continuous can be any value, like someone’s height “6.343 ft tall”.
what is a quantitative variable?
Quantitative 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 etc. Warning: numbers like zip codes, phone numbers, jersey numbers on an athlete and phone numbers are categorical…
what do we sometimes call a categorical variable?
qualitative
what is a continuous variable?
continuous can take on any value (along a continuum), like age. 14.237 years old.
What is a discrete variable?
Discrete are generally countable (integers). Like SAT score, IQ, number of days absent. There is no 611.3 SAT Verbal score.
What is a random sample?
When and appropriate randomizing procedure is used to choose a sample.
What is frequency?
How often something comes up
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)
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
Make a guess as to what cumulative relative frequency is?
It is the ADDED up PERCENTAGES.. For the candy example, with the 25 pieces sold at 10 the first hour, 5 the second, 3 the third and 7 the last hour, the cumulative relative frequency was 10, 15, 18, 25? change these to percents by dividing each by 25 and you get .4, .6, .64, 1.00
How do you find relative frequency?
just divide frequency by TOTAL
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 generally tough)..
What does a measure of “central tendency” try to tell us about?
meant to convey the “general idea” of where most data values lie
What is the mean?
the old average we used to calculate. It is the balancing point of the histogram
What is the difference between population mean and sample mean?
population mean is the mean of a population, it is a parameter, sample mean is a the mean of a sample, it is a statistic. We take sample means to make inferences about population means. We take statistics to make inferences about parameters.
What symbols do we use for population mean and sample mean?
mu for population mean (parameter), x-bar for sample mean (statistic)
How can you think about the mean and median and mode?
mean is balancing point of histogram, median splits the area of the histogram in half, modes are the peaks
What is the median?
the middlest number (always in the (n+1)/2 position), it splits area of a histogram in half
What is the mode?
the most common, or the peaks of a histogram. (sometimes the mode doesn’t even appear.. its just where the data is gathered around)
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 is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc).
How are mean, median and mode positioned in a skewed left distribution(negatively skewed)?
goes in that order from left to right. Mean-median-mode
How are mean, median and mode positioned in a skewed right distribution(positively skewed)?
goes in the opposite order.. Mode-median-mean
Who chases the tail?
The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean chases the tail….. and outliers
