Summer Stats

Question 1

What is variability?

Answer 1

Differences? How things differ. There is variability everywhere. We all look different, like different things, act differently. Statisticians look at these differences.

Question 2

What are 2 branches of AP Stats?

Answer 2

Inferential and Discriptive

Question 3

What are descriptive statistics?

Answer 3

Tell me what you got! Describe your data that you collected through pictures and summaries like mean, median, standard deviation, range, etc

Question 4

What are inferential statistics?

Answer 4

Looking at your data (sample) and making an educated guess about the whole. It’s like tasting soup - a little bit (sample) can tell you a lot about the whole pot (population).

Question 5

Compare descriptive and inferential statistics

Answer 5

Descriptive statistics tells you about the data that you have and inference uses that data to draw conclusions about the populations.

Question 6

What is data?

Answer 6

A collection of values or categories measured. You may count the number of words someone can type per minute like 30, 57, 25, or you may collect yes or no answers to a question posed to a group of people.

Question 7

What is a population?

Answer 7

The entire group you’re interested in = all. It can be massive, such as “all teenagers in the US” or it can be small such as “all juniors in our high school”.

Question 8

What is a sample?

Answer 8

A small part of the population = some. We use the sample to learn about the population.

Question 9

What is a statistic?

Answer 9

A value that characterizes a sample: sample mean, sample proportion, sample median, sample range, etc

Question 10

What is a parameter?

Answer 10

A value that characterizes a population: population mean, population proportion, population median, population range, etc

Question 11

Compare data to statistics

Answer 11

Data is the individual values we measure on each member of our sample, the little things we collect, like “your GPA”, while statistics are numerical summaries (mean, median, etc) of that data.

Question 12

Compare data to parameters

Answer 12

Data is the individual values we measure on each member of our sample, the little things we collect, like “how tall you are”, while parameters are summaries (mean, median, etc) of the whole population. In other words, we collect data (i.e. we take a sample), we calculate summaries (statistics) that we then use to estimate the values of the parameters which represent the population.

Question 13

We are interested in the average wait time at Wendy’s drive through in our neighborhood. You randomly sample cars at Wendys one afternoon and find that the average wait time is 2.7 minutes. What is the sample? What is the population? What is the parameter? What is the statistic? What is the data?

Answer 13

The sample is formed by the cars you “sampled”. The population is formed by all cars driving through at Wendy’s ever and forever, all of them. The parameter of interest is the average wait time for all cars at this Wendy’s. You will NEVER know this number. The statistic is the sample mean of 2.7 minutes wait time. We use this 2.7 to estimate and make inferences about the whole population. The data is formed by all the individual times you collected: 3.5 minutes, 1.9 minutes, 5 minutes, and so on.

Question 14

What is a census?

Answer 14

Data collected on all individuals of the population - we do it every 10 years. Can we collect data from ALL individuals?

Question 15

Does a census make sense?

Answer 15

For a small population, like our school, yes, but not if we want to collect data on all girls in the US

Question 16

What is the difference between parameters and statistics?

Answer 16

Although both are single numbers summarizing a large group of numbers, pppp parameters come from pppp populations and ssss statistics come from ssss samples.

Question 17

If I ask 25 random students how many pets they have and one of them says 7, then the number 7 is?

Answer 17

a datum, or a data value, or a data point

Question 18

If I ask 25 random students how many pets they have and the average number of pets is 7 pets, then 7 is____

Answer 18

a statistic (summary of the sample)

Question 19

If I ask 25 random students what how many pets they have and I do this because I want to know the true average number of pets the students in our school have, the true average number of pets is considered ______

Answer 19

a parameter, a one number summary of the population.

Question 20

What is the difference between a sample and a census? ?

Answer 20

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 21

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

Answer 21

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 of interest.

Question 22

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 22

If you are tasting soup, then the flavor of each individual thin 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 soup, which would be the PARAMETER. Notice you are interested in the parameter to begin with…..that is why you take a sample.

Question 23

What are random variables?

Answer 23

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 24

What is the difference between quantitative and categorical variables?

Answer 24

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

Question 25

What is the difference between quantitative and categorical data?

Answer 25

The data is the actual gathered measurements. If it’s eye color, then the data would look like “blue, green, green, brown, brown, blue, blue…etc” - words for categorical. If it’s weight, then the data would look like “100, 156, 238, 167, 155, …etc’ - numbers for quantitative.

Question 26

What is the difference between discrete and continuous variables?

Answer 26

Discrete can be counted, like “number of pets a student has” - they are generally integers (except shoe size), while continuous can take any real number value such as the time it takes to complete an obstacle course, like 5.324 minutes

Question 27

What is a quantitative variable?

Answer 27

Quantitative variables are numeric like: height, age, number of M&Ms, SAT
score

Question 28

What is a categorical variable?

Answer 28

Categorical variables are like categories: Blonde, Listens to Hip Hop, Female, yes,
no … etc.

Question 29

What do we sometimes call a categorical variable?

Answer 29

Qualitative

Question 30

What do we sometimes call a quantitative variable?

Answer 30

Numerical

Question 31

What is quantitative data?

Answer 31

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

Question 32

What is categorical data?

Answer 32

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

Question 33

What is a random sample?

Answer 33

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 34

What is frequency?

Answer 34

How often something comes up

Question 35

Data or datum?

Answer 35

datum is singular .. Like “hey dude, come see this datum I got from this rat!” data is the plural .. “hey look at all these data Edgar got from those chipmunks over there!!”

Question 36

What is a frequency distribution?

Answer 36

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

Question 37

What is meant by relative

frequency?

Answer 37

The PERCENT of time something comes up

Question 38

How do you find relative frequency?

Answer 38

just divide frequency by TOTAL. … frequency relative to the whole

Question 39

What is meant by cumulative frequency?

Answer 39

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 for the first hour, 15 for the first 2 hours, 18 for the first 3 hours, 25 for all 4 hours….so eventually, you’d cumulate the whole data set

Question 40

Make a guess as to what relative cumulative frequency is …

Answer 40

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 41

What is the difference between a bar chart and a histogram

Answer 41

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

Question 42

What is the mean?

Answer 42

It’s what your parents/grandparents would call average. It is the balancing point of the histogram

Question 43

What is the difference between a population mean and a sample

Answer 43

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 44

What symbols do we use for population mean and sample mean?

Answer 44

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

Question 45

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

Answer 45

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

Question 46

What is the median?

Answer 46

The number in the middle after ordering the data; it splits area in half (always in the position (n+1/2)

Question 47

What is the mode?

Answer 47

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 48

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

Answer 48

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 49

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

Answer 49

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 50

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

Answer 50

It goes in order from left to right: Mean-Median-Mode

Question 51

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

Answer 51

It goes in order from left to right: Mode-Median-Mean

Question 52

Who chases the tail?

Answer 52

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