AP Statistics Summer Vocab

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 Stats?

Answer 3

Inferential and descriptive

Question 4

What are DESCRIPTIVE STATS?

Answer 4

Describe what you see using pictures or summaries (mean, mode, median, range)

Question 5

What are INFERENTIAL STATS?

Answer 5

Use your data to make a statement about the big picture (ex. Tasting soup, a spoonful is a sample, to determine what is in the whole pot, the population)

Question 6

Descriptive vs. Inferential

Answer 6

Descriptive describes the data you have, inferential uses that data to make a statement about the whole population

Question 7

What is data?

Answer 7

The information collected from each individual

Ex) You ask people if they like the Red Sox → each answer (yes or no) is a piece of data

Ex) You ask people their height → each person’s height is a piece of data

Question 8

What is a population?

Answer 8

The group you are interested in. It can be big (ex. Every adult in the US) or small (ex. Each student in my AP Stats class)

Question 9

What is a sample?

Answer 9

A subset or small collection of your population. We usually sample because our population is too big to do a census.

Question 10

What is a census?

Answer 10

When you literally collect data from every individual in your population. It’s easy to do if the population is small (ex. Everyone in a classroom), but difficult if it is large (ex. Everyone in Massachusetts).

Question 11

What is a parameter?

Answer 11

A summary of your population’s data. (Parameter → Population)

Question 12

What is a statistic?

Answer 12

A summary of your sample (Statistic → Sample)

Question 13

Compare data to statistics

Answer 13

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 14

Compare data to parameters

Answer 14

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 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 categorical example

Answer 16

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 using quantitative summaries like “the average breath holding time in the sample was 52.4 seconds” example and a parameter would be “the average breath holding time in the population was 52.4 seconds”

Question 17

Parameter vs. Statistics

Answer 17

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

Question 18

Sample vs. Census

Answer 18

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 19

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

Answer 19

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 20

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 20

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 21

What are random variables?

Answer 21

The categories or type of data collected in a random sample (ex. If you sample a group of people, their eye color, heights, age, etc. are all random variables).

Question 22

What is the difference between quantitative and categorical variables?

Answer 22

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

Question 23

What is the difference between categorical/qualitative and quantitative variables?

Answer 23

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.

Question 24

What is the difference between discrete and continuous variables?

Answer 24

Discrete can be counted, like “number of cars sold” they are generally integers (you wouldn’t sell 9.3 cars) but can not always (shoe size is discrete but you have 9, 9 ½ ,10, 10 ½ ,etc), while continuous would be something like weight of a mouse… 4.344 oz.

Question 25

What is a quantitative variable?

Answer 25

Can be measured numerically (height, SAT score, GPA, etc)

Question 26

What is a qualitative/categorical variable?

Answer 26

When data is measured by a category (hair color, listens to hip hop, ethnicity, gender, etc)

Question 27

What is quantitative data?

Answer 27

The actual numbers gathered from each subject or unit (ex. 200 lbs, 3.6 GPA, 1240 SAT score, etc)

Question 28

What is categorical data?

Answer 28

The actual category from a subject (ex. Blonde, male, listens to jazz, freshman, etc)

Question 29

What is a random sample?

Answer 29

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.

Question 30

What is frequency?

Answer 30

How often something happens

Question 31

What is a frequency distribution?

Answer 31

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

Question 32

What is meant by relative frequency?

Answer 32

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

Question 33

How do you find relative frequency?

Answer 33

Just divide frequency by TOTAL….

Question 34

What is meant by cumulative frequency?

Answer 34

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 35

What is relative frequency?

Answer 35

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 36

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

Answer 36

Bar charts are for categorical data (bars don’t touch) and histograms are for quantitative data (bars touch)

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 symbol do we use for population mean?

Answer 39

µ (Mu)

Question 40

What symbol do we use for sample mean?

Answer 40

x̄ (x-bar (lowercase x, not capital))

Question 41

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

Answer 41

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

Question 42

What is the median?

Answer 42

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

Question 43

What is mode?

Answer 43

The most common data value or category, the peak of a histogram

Question 44

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

Answer 44

It is not RESILIENT, it is impacted by skewness and outliers.

Question 45

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

Answer 45

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 46

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

Answer 46

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 47

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

Answer 47

Goes in that order from left to right → Mean-median-mode

Question 48

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

Answer 48

Goes in the opposite order… Mode-median-mean

Question 49

What chases the tail in histogram?

Answer 49

The mean chases the tail