Summer Work

Question 1

What is statistics?

Answer 1

The study of variability

Question 2

What is variability?

Answer 2

Differences… how things differ. There is variability everywhere.. We all look different, act different, have different preferences… Statisticians look at these differences.

Question 3

What are 2 branches of stats

Answer 3

Inferential and Descriptive

Question 4

What are descriptive stats

Answer 4

Tell me what you got! Describe to me the data that you collected, use pictures or summaries like mean, median, range, etc…

Question 5

What are inferential stats

Answer 5

Look at your data, and use that to say stuff about the BIG PICTURE… like tasting soup, a little taste tells you about the whole pot… a little sample can tell you a lot about the big pot of soup (the population)

Question 6

Compare Descriptive and Inferential stats

Answer 6

Descriptive explains the data that you have, inference uses that data you have to try to say something about an entire population….

Question 7

What is data

Answer 7

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”

Question 8

What is a population

Answer 8

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”

Question 9

What is a sample

Answer 9

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

Question 10

Compare population to samples

Answer 10

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.

Question 11

Compare data to statistics

Answer 11

Data is each little bit of information collected from the subjects…. They are the INDIVIDUAL little things we collect… Statistics are when 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”

Question 12

Compare data to parameters

Answer 12

Data is each little bit of information collected from the subjects…. They are the INDIVIDUAL little things we collect… parameters are the numbers that summarize an entire population

Question 13

What is a parameter

Answer 13

A numerical summary of a population. Like a mean, median, range… of a population

Question 14

What is a statistic

Answer 14

A numerical summary of a sample. Like a mean, median, range… of a sample.

Question 15

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

Answer 15

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.

Question 16

Compare DATA-STATISTICPARAMETER using categorical examples

Answer 16

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.”

Question 17

Compare DATA-STATISTICPARAMETER using quantitative examples

Answer 17

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”

Question 18

What is a census

Answer 18

Like a sample of the entire population, you get information from every member of the population

Question 19

Does a census make sense

Answer 19

A census is ok for small populations (like Mr. Nystrom’s students) but impossible if you want to survey “all US teens”

Question 20

What is the difference between a parameter and a statistic

Answer 20

BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS…. But pppp parameters come from pppp populations… sss statistics come from sss statistics.

Question 21

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 ____

Answer 21

a datum, or a data value

Question 22

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 _______

Answer 22

statistic (it is a summary of a sample)

Question 23

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 ______

Answer 23

parameter, a one number summary of the population. The truth. AKA the parameter of interest.

Question 24

What is the difference between a sample and a census

Answer 24

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.

Question 25

Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest

Answer 25

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).

Question 26

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__________

Answer 26

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.

Question 27

What are random variables

Answer 27

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.

Question 28

What is the difference between quantitative and categorical variables

Answer 28

Quantitative variables are numerical measures, like height and IQ. Categorical are categories, like eye color and music preference

Question 29

What is the difference between quantitative and categorical data

Answer 29

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 simply “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.

Question 30

What is frequency

Answer 30

how often something comes up

Question 31

data or datum

Answer 31

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!!”

Question 32

what is a frequency distribution

Answer 32

A table, or a chart, that shows how often certain values or categories occur in a data set.

Question 33

what is meant by relative frequency

Answer 33

The PERCENT of time something comes up (frequency/total)

Question 34

how do you find relative frequency

Answer 34

just divide frequency by TOTAL….

Question 35

what is meant by cumulative frequency

Answer 35

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

Question 36

Make a guess as to what relative cumulative frequency is…

Answer 36

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.

Question 37

what is the mean

Answer 37

the old average we used to calculate. It is the balancing point of the histogram

Question 38

What is the difference between a population mean and a sample mean

Answer 38

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.

Question 39

what is the median

Answer 39

the middlest number, it splits area in half (always in the POSITION (n+1)/2 )

Question 40

what is the mode

Answer 40

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

Question 41

when do we often use mode

Answer 41

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…).

Question 42

When we say “the average teenager” are we talking about mean, median or mode

Answer 42

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.