AP Summer Assignment

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 the two branches of AP Statistics?

Answer 3

Descriptive and Inferential

Question 4

What are descriptive statistics?

Answer 4

Describing the data that was collected using pictures (graphs) or summaries such as mean, median, range, etc…

Question 5

What are inferential statistics?

Answer 5

Look at the data that was collected from a sample and use that to make a statement about the big picture (the population)

Question 6

Compare descriptive and inferential statistics

Answer 6

Descriptive explains the data that you have, inferential statistics use that data to try and say something about the entire population.

Question 7

What is data?

Answer 7

Any collected information. Generally every measurement.
For example, if you are taking a survey about if students like pizza… the data might be “yes, yes, no, no, yes”. If it is the number of pushups someone can do in a minute, the data might be “20, 15, 2, 16”

Question 8

What is a population?

Answer 8

The group that you are interested in. Sometimes it is large (US Adults) sometimes it is small (AP Stats students at Renaissance)

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 sample

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… 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… 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 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-STATISTIC-PARAMETER using a categorical example

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 those sampled preferred tacos” and a parameter would be “42% of population
preferred tacos.”

Question 17

Compare DATA-STATISTIC-PARAMETER using a quantitive example

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 taking a census make sense?

Answer 19

A census is ok for small populations (like Mr. Creeden’s students) but impossible/very costly 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 parameters come from populations… statistics come from samples

REMEMBER, MATCH P TO P AND S TO S

Question 21

If I take a random sample of 20 hamburgers from McDonald’s 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 data value

Question 22

If I take a random sample 20 hamburgers from McDonald’s 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 (a single number summary of a sample)

Question 23

If I take a random sample of 20 hamburgers from McDonald’s 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 McDonald’s, the true average number of pickles is considered a ______?

Answer 23

Parameter - it is a one-number summary of a population. Also, 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 that shows their meaning: 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

Random variables are outcomes from chance processes.

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 time spent sleeping. Categorical are groups, like eye color and music preference

Question 29

What is the difference between quantitative and categorical data?

Answer 29

Quantitative data takes the form of numbers WITH UNITS (5 pounds, three feet, etc) and a meaningful average can be taken. Categorical data is often words and an average can not be taken (no such thing as average favorite color)

Question 30

What is the difference between discrete and continuous variables?

Answer 30

Discrete variables can be counted and can achieve only a certain number of possible values (number of cars sold, shoe size, etc). They often are whole values.

Continuous variables can be any value in a given range. For example time spent holding your breath can have any value between 0 and 10 minutes (eg 24.4342 seconds)

Question 31

What is a quantitative variable?

Answer 31

Quantitative variables are numeric and have units (height, weight, number of siblings, etc)

Question 32

What is a categorical variable?

Answer 32

Qualitative variables that divide a group such as hair color, favorite type of music, etc.

Question 33

What do we sometimes call categorical variables?

Answer 33

Qualitative

Question 34

What is quantitative data?

Answer 34

The actual numbers gathered from each subject. 200 pounds, 67 beats per minute.

Question 35

What is categorical data?

Answer 35

The actual individual category from a subject

Question 36

What is a random sample?

Answer 36

When you choose a sample through an actually random process (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.

Question 37

What is frequency

Answer 37

How often a data value appears in a set of data

Question 38

What is the difference between data and datum?

Answer 38

Datum is singular (one persons answer to the question “Do you like salt and vinegar chips?”)

Datum is plural (the collection of 40 peoples answer to the question “do you like salt and vinegar chips?)

Question 39

What is a frequency distribution.

Answer 39

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

Question 40

How do you determine relative frequency

Answer 40

Divide frequency by total.

Question 41

What is meant by relative frequency.

Answer 41

The percent of time a value or category shows up.

Question 42

What is meant by cumulative frequency

Answer 42

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 43

What is relative cumulative frequency?

Answer 43

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 44

What is the difference between a bar chart and a histogram?

Answer 44

Bar charts (bars dont touch) are used for categorical data. Histograms (bars touch) are used for quantitative data.

Question 45

What is the mean

Answer 45

Commonly known as the average. It is the balancing point of a histogram or dotplot.

Question 46

What are the symbols for population mean and sample mean?

Answer 46

Mu (μ) for population mean (parameter), x-bar ( ̅x) for sample mean (statistic)

Question 47

How can you think about the mean and median to remember the difference when looking at a histogram?

Answer 47

mean is balancing point of the histogram, median splits the area of the histogram in half

Question 48

What is the median?

Answer 48

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

Question 49

What is the mode?

Answer 49

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

Question 50

When do we often use mode?

Answer 50

With categorical variables. For instance, to describe the average teenager’s preference, we often speak of what “most” students chose, which is the mode. It also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc…).

Question 51

Why don’t we always use the mean, we’ve been calculating it all of our life?

Answer 51

The mean is not a resistant measure and is easily affected by skew. For example, if I sample 5 people randomly and try to determine the average age, the median would give me a more accurate idea of the sample if they were 21, 23, 23, 25, and 82 years old.

Question 52

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

Answer 52

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.

Question 53

what is a clear example of where the mean would change but median wouldn’t? (this would show its
resilience)

Answer 53

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.

Question 54

How are mean, median, and mode positioned in a skewed left histogram?

Answer 54

goes in that order from left to right. Mean-median-mode

Question 55

How are mean, median, and mode positioned in a skewed righthistogram?

Answer 55

Goes in opposite order. Mode - Median - Mean

Question 56

Who chases the tail?

Answer 56

The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean chases the tail… and outliers…….