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 2 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 INFERENTIAL STATS?

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)

<p>Compare Descriptive and Inferential STATS</p>

<p>Descriptive tells youabout the data that you have, inference uses that data you have to try to say something about an entire population?.</p>

What is data?

Any collected information. Generally each little measurement? Like, if it is a survey about liking porridge? 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 a population?

the group you’re interested in. 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 sample?

A subset of a population, often taken to make inferences about the population. We calculate statistics from samples.

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.

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”

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.

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 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.?

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?

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 students) but impossible if you want to survey “all US teens”

<p>What is the difference between a parameter and a statistic?</p>

<p>BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS?. But pppp parameters come from pppp populations? sss statistics come from ssss samples.</p>

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 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. (t 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 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.

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.

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 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 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.

What is a quantitative variable?

Quantitative variables 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, yes, no? etc.

What do we sometimes call a categorical variable?

qualitative

What is quantitative data?

The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.

What is categorical data?

The actual individual category from a subject, like “blue” or “female” or “sophomore”

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

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 those chipmunks over there!!”

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

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.

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 symbols do we use for population mean and sample mean?

Mu for population mean, xbar for sample mean.

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 the mode?

the most common, or the peaks of a histogram. We often use mode with categorical data

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?).

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?

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.