FIXED UNIT 1 TEST - in order Flashcards
This is repaired. Hopefully no more typos/mistakes.
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 contents of the entire spoon is a ______.. The flavor of all of that stuff together on the spoon 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 contents of the entire spoon is a SAMPLE. The flavor of all of that stuff together on the spoon 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.
Which is more sensitive to outliers and skewed? Mean, median. Sd or IQR?
Mean and SD are most influenced by outliers. median and IQR are RESISTANT, RESILIENT, ROBUST!!
Can numbers be CATEGORICAL?
sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.
Compare data to parameters
Data is each little bit of information collected from the subjects. They are the INDIVIDUAL little things we collect, like “5, 7, 9” . if we have all of the data from the population, then we can summarize it by finding the average and that would be called a parameter. (if we only had a sample then the summary is called a statistic)
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 “42% of population preferred tacos.” Notice that for categorical variables, the categories are words and the statistics and parameters are percents.
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”
Compare Descriptive and Inferential STATS
Descriptive explains you about the data that you have, inference uses that data you have to try to say something about an entire population….
Compare population to sample
populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.
data or datum?
datum is singular, Like “hey dude, come see this datum I got from this rat!” data is the plural, “hey look at all that data Edgar got from his brussel sprouts”
Does a census make sense?
A census is ok for small populations (like Mr. Nystrom’s students) but impossible if you want to survey “AVERAGE TREE HEIGHT IN THE US”
How do you find relative frequency?
PERCENTS- just divide frequency by TOTAL. a percent is relative to the whole.
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. It is a summary of a sample.
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 had 9 pickles, then the number 9 from that burger would be called ____?
a datum, or a data value.
If I take a random sample of 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.
If you are calculating a mean, then you must have ______ data
quantitative
if you are calculating a percent, then you must have _____ data
categorical
Make a guess as to what relative cumulative frequency is…
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.
Percents are also known as ______
proportions
What is the difference betwen a categorical variable and categorical data?
If you wanted the percent of cape cod dogs that are brown, the variable would be “dog color” and the data would be: brown, black, white, mixed, brown
What is the is the difference between quantitative data and quantitative variables?
If you want average cape cod dog weight… the variable would be “WEIGHT”– the data are the individual weights.. the actual numbers: 2.3lbs, 5.5 lbs.
What is the difference between popluation of interest, variable of interest and parameter of interest?
If we want the average weight of cape cod dogs, population is cape cod dogs, the variable is the weight, the parameter is the mean weight. If we wanted the percent that are brown, the population would still be cape cod dogs, the variable would be dog color and the parameter would be % brown.
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 population parameter.
What are 2 major branches of AP STATS?
Inferential and Descriptive
What are DESCRIPTIVE STATS?
Tell me what you got! Describe to me the data that you collected, use pictures or summaries like mean, median, range, etc
What are random variables?
ANY QUALITY MEASURED FROM A RANDOMLY CHOSEN SUBJECT. f you randomly choose people from a list, then any quality measured.. their hair color, height, weight can be considered random variables. Same thing with cars.. If you randomly pick them then any quality measured is a random variable.
What do we sometimes call a categorical variable?
qualitative
What is a categorical variable? Compare to categorical data.
Categorical (or qualitative) variables are the categories you are interested in like “hair color” and “music preference”. The data are the measureds from individuals like: SUV, sedan, Listens to Hip Hop, Female, yes, no, etc.
What is a census?
Like a sample of the entire population, you get information from every member of the population
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 a parameter?
A numerical summary of a population. Like a mean, median, range of a population
What is a population?
(not necessarily people). the group of stuff you’re interested in. It could be “bags of potato chips..” Sometimes it’s big, like “all teenagers in the US” other times it is small, like “all AP Stats students in my school”
What is a quantitative variable? Compared to quantitative data?
Quantitative variable are the things your are interested in like: Height, age, price, number of cars sold, SAT score. Quantitative data are the actual heights or ages from individuals: 54” , 2 years, $ 34.99
What is a random sample?
When you choose a sample by rolling dice, choosing names from a hat, or other TRULY RANDOM generated sample. Humans can’t really do this well without the help of a calculator, cards, dice, or slips of paper.
What is categorical data?
The actual individual category from a subject, like “sedan” or “blue” or “female” or “sophomore”
What is data?
Any collected information. Generally each little measurement, Like, if it is a survey about liking porridg, the data might be “yes, yes, no, yes, yes” if it is the number of saltines someone can eat in 30 seconds, the data might be “3, 1, 2, 1, 4,3 , 3, 4”
What is frequency?
How often something comes up
What is INFERENTIAL STATISTICS?
The part of the course where you look at your data and use that to say stuff about the BIG PICTURE. like tasting soup. a little sample can tell you a lot about the big pot of soup (the population)
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 meant by relative frequency?
The PERCENT of time something comes up (frequency/total)
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
What is the couse “Statistics” about?
The study of variability. Not just how individual subjects vary, but later on how two different samples from the same population can get different summaries. We later look at how statistics vary from sample to sample.
What is the difference between a bar chart and a histogram
bar charts are for categorical data (bars don’t touch and can often be in any order) and histograms are for quantitative data (bars usually touch and x axis is in order)
What is the difference between a parameter and a statistic?
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS. But pppp parameters come from pppp populations, sss statistics come from ssss samples
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 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.
What is the difference between categorical VARIABLES and categorical DATA?
The Variable is the overall category. Like “EYE COLOR”. The data is the actual measurement from the subjects. Like “blue, brown, blue”
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), while continuous would be something like weight of a mouse. 4.344 oz. Summaries of discreet variables will often be decimals.
What is the difference between quantitative and categorical data?
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 quantitative and categorical variables?
Quantitative variables are numerical measures, like height and IQ. Categorical are categories, like eye color and music preference
What is variability?
Differences, how things differ. There is variability everywhere. We all look different, act different, have different preference. Statisticians look at these differences. SAMPLE STATISTICS ALSO VARY FROM SAMPLE TO SAMPLE.
What parameter do you usually calculate for categorical data?
%, percent, or proportion
What parameters do you usually calculate for quantitative data?
mean (and sd) or median (and IQR)
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
What symbols do we use for population proportion (%) and sample proportion (%)?
p for population and p-hat for sample
What symbols do we use for population standard deviation and sample standard deviation?
Sigma for population and s for sample.
When can you round?
AT THE VERY END!!! (keep 3 digits until end!)
How could you use mode with categorical variables?
With categorical variables. For instance, to describe the average teenagers preference, we often speak of what “most” students chose, which is the mode. “the average teenager likes mexican food.” It is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc…).
When drawing a graph or chart, what do you have to remember to do?
LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! “Figure 1: Age and Food Preference”
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.
You calc percents with ___ data
categorical
You calc means/SD with ___ Data
quantitative
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…….
Another name for “skewed right” is
positively skewed
How are mean, median and mode positioned in a skewed left histogram?
goes in that order, mean median mode (mean chases the tail to balance the histogram)
How are mean, median and mode positioned in a skewed right histogram?
mode- median- mean (mean chases the tail)
How can you think about the mean, median and mode remember the difference when looking at a histogram?
mean is balancing point of histogram, median splits the area of the histogram in half, mode is the highest point or points
If a distribution is skewed left, what will be greater, the mean or median? WHY?
Median. The mean moves left to keep balance.
If a distribution is skewed right, what will be greater, the mean or median? WHY?
Mean. The mean moves further to the right to keep balance.
If the mean is above the median, the distribution may be
skewed right or positively skewed, the mean follows the tail
