Unit 1

Question 1

What is variability?

Answer 1

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

Question 2

What is data?

Answer 2

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 3

What is a population?

Answer 3

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 4

What is a sample?

Answer 4

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

Question 5

Compare population to sample

Answer 5

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 6

Compare data to statistics

Answer 6

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 7

Compare data to parameters

Answer 7

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 8

What is a parameter?

Answer 8

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

Question 9

What is a statistic?

Answer 9

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

Question 10

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 i

Answer 10

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 11

Compare DATA-STATISTIC-PARAMETER using categorical example

Answer 11

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 12

Compare DATA-STATISTIC-PARAMETER using quantitative example

Answer 12

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 13

What is a census?

Answer 13

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

Question 14

Does a census make sense?

Answer 14

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

Question 15

What is the difference between a parameter and a statistic?

Answer 15

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

Question 16

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 16

statistic. (t is a summary of a sample.)

Question 17

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 bun

Answer 17

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

Question 18

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

Answer 18

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 19

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

Answer 19

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 20

What are random variables?

Answer 20

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 21

What is the difference between quantitative and categorical variables?

Answer 21

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

Question 22

What is the difference between quantitative and categorical data?

Answer 22

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 23

What is the difference between discrete and continuous variables?

Answer 23

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.

Question 24

What is a quantitative variable?

Answer 24

Quantitative variables are numeric like: Height, age, number of cars sold, SAT score

Question 25

What is a categorical variable?

Answer 25

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

Question 26

What is quantitative data?

Answer 26

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

Question 27

What is categorical data?

Answer 27

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

Question 28

What is a random sample?

Answer 28

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 29

What is frequency?

Answer 29

How often something comes up

Question 30

What is a frequency distribution?

Answer 30

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

Question 31

What is meant by relative frequency?

Answer 31

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

Question 32

How do you find relative frequency?

Answer 32

just divide frequency by TOTAL.

Question 33

What is meant by cumulative frequency?

Answer 33

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 34

What is the difference between a bar chart and a histogram

Answer 34

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

Question 35

What is the mean?

Answer 35

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

Question 36

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

Answer 36

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 37

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

Answer 37

Mu for population mean, xbar for sample mean.

Question 38

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

Answer 38

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

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

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

Answer 41

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

Question 42

When we say the average teenager are we talking about mean

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.

Question 43

Q: How can you get a parameter? A: By taking a ___________

Answer 43

Census

Question 44

When drawing a graph or chart, what do you have to remember to do?

Answer 44

LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! “Figure 1: Age and Food Preference”

Question 45

What is the IQR?

Answer 45

Interquartile range… a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.

Question 46

What is a CUMULATIVE FREQUENCY GRAPH?

Answer 46

An OGIVE. It shows the added up totals as you go left to right.

Question 47

What is a “percentile?”

Answer 47

It tells you the percent of data at or BELOW a certain value

Question 48

where are the “outlier fences?”

Answer 48

1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.

Question 49

What is the five number summary?

Answer 49

min, Q1 , Q2(median), Q3 and max

Question 50

How do you find Q1 and Q3?

Answer 50

Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)

Question 51

What percentile is Q3?

Answer 51

75th

Question 52

How do you describe distributions (histograms)?

Answer 52

Shape-Outliers-Center-Spread-SOCS

Question 53

How can you describe spread?

Answer 53

range, IQR, stand dev, variance, or simply say: From here, to about here

Question 54

How can you describe shape?

Answer 54

TWO THINGS: modes and symmetry.unimodal, bimodal, multimodal AND uniform, symmetric, skewed

Question 55

How do you describe CENTER for bimodal or multimodal?

Answer 55

talk about the modes (the lumps, the clusters)

Question 56

How do you describe CENTER for skewed or distributions with outliers?

Answer 56

use the MEDIAN

Question 57

How do you describe CENTER for unimodal and symetric distributions?

Answer 57

use the MEAN

Question 58

How do you descrive SPREAD for unimodal and symmetric distributions?

Answer 58

use the standard deviation

Question 59

How do you describe SPREAD for skewed distributions (or distributions with outliers?)

Answer 59

Use the IQR

Question 60

How do you describe SPREAD for bimodal or multimodal?

Answer 60

talk about the outer edges of the clusters “from here to here” or use the IQR.

Question 61

What does SOCS stand for?

Answer 61

Gaps Shape Outliers Center Spread (put on your gsocs when comparing distributions) be sure to talk about each one clearly (make a list)

Question 62

Give a quick example of associated variables

Answer 62

A higher percentage of boys play video games than girls so we say “gender and video game playing are associated” or “gender and video game playing are not independent”

Question 63

what is a conditional distribution?

Answer 63

A distribution with a condition (within the table), along only one row or one column… NOT IN THE MARGINS. You are given a condition.. Then read along that row or column.

Question 64

What percent of the data is above Q3?

Answer 64

25%

Question 65

What percent of the data is between Q1 and Q3?

Answer 65

the middle 50%. That is the IQR

Question 66

What is Q2 also known as?

Answer 66

the median

Question 67

What percent of the data is below Q2?

Answer 67

50%

Question 68

What is a standard deviation?

Answer 68

average (typical) distance to the mean. It is how far you expect a random value to be away from the middle.

Question 69

What is a Z score?

Answer 69

The number of standard deviaiton away from the mean

Question 70

For information purposes, which gives LEAST… stem-leaf, histogram or box-whisker?

Answer 70

Box/Whisker, BE CAREFUL. you really don’t know how things are distributed. The box and whisker give a very GENERAL look.

Question 71

What are the percentiles for Q1, med, and Q3?

Answer 71

25, 50 and 75

Question 72

How do students often mix up IQR and St. Dev

Answer 72

They INCORRECTLY think that Q1 is 1sd below the mean and Q3 is 1sd above the mean. THIS IS NOT TRUE!!! Q1 is only .67 sd above the mean and Q2 is .67 below

Question 73

Does the IQR capture 68% of the data?

Answer 73

NO. it catches the middle 50%.

Question 74

What percentile is the median (aka Q2)?

Answer 74

50th

Question 75

What percent of the data is between Q1 and Q3?

Answer 75

50%

Question 76

If the mean is above the median, the distribution may be

Answer 76

skewed right… the mean follows the tail

Question 77

Another name for “skewed right” is

Answer 77

positively skewed

Question 78

How many SD wide is the IQR in a normal distribution?

Answer 78

NOT 2!!!! Think about it. The middle 68% is 2 sd wide, since the IQR is only the middlest 50% it must be less than 2. try [invnorm(.75)] x2. You find that it is only 1.35 SD wide if the distribution is nearly normal.

Question 79

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

Answer 79

Mu for population mean, xbar for sample mean.

Question 80

What symbols do we use for population standard deviation and sample standard deviation?

Answer 80

Sigma for population and s for sample.

Question 81

What percent of the data is above Q3?

Answer 81

25%

Question 82

What percent of the data is below the median?

Answer 82

50%

Question 83

What is the difference between categorical VARIABLES and categorical DATA?

Answer 83

The Variable is the overall category. Like “EYE COLOR”. The data is the actual measurement from the subjects. Like “blue, brown, blue”

Question 84

Can numbers be CATEGORICAL?

Answer 84

sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes… these are categorical.

Question 85

what is the emperical rule?

Answer 85

mean 68-95-99.7 yeah!

Question 86

are any populations actually normal?

Answer 86

no, nothing is normal, just normalish. The only normal thing is the model we use.

Question 87

If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?

Answer 87

Median (center) and IQR (spread)

Question 88

What is the variance?

Answer 88

The average squared distance to the mean. Or the SD2 (It is the SD before you take the square root, so it is the stuff under the radical in the formula)

Question 89

What percentile is Q1?

Answer 89

25th

Question 90

Why are there different standard deviation formulas for population and sample? Arent they the same thing?

Answer 90

Both equations are actually doing the same thing. They both attempt to calculate the true population proportion. When you have all of the data from the population you just divide by n and get the actual SD. BUT If you only have a sample then you are using that to make a guess (inference) at what the population standard deviation is.. What happens is that samples tend to have less spread so their SD underestimates the population, BUT, when you divide by n-1 instead of n, It gives you a better estimate of what the population standard deviation is.

Question 91

Give a simple example showing that adding a constant doesn’t change the spread, but changes the center. (this always happens)

Answer 91

Data set: 1,2,3,4,5 Spread (range):4, Center: 3 add three and get new data set: 3,4,5,6,7 spread:4 Center: 5 (center went up, spread stayed the same). The IQR and SD will stay the same, but median and mean go up 3. Called shifting, or sliding the data.

Question 92

what happens if you multiply all of a data set by a constant? Think of an example

Answer 92

it is scaled Both center and spread are impacted. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed. Consider 1,2,3,4,5 mean of 3 and range of 4. Now multiply by 3: 3,6,9,12,15 and you get a mean of 9 and a range of 12… both multiplied by three.

Question 93

what happens if you ADD a constant to each value in a data set?

Answer 93

it is SHIFTED only. Does not impact spread. This effects all of the data values and measures of center (mean, med) and quartiles, deciles, etc, IT DOES NOT CHANGE THE SPREAD! (IQR, St Dev, Range all stay the SAME).

Question 94

what is a clear example of the medians resiliance and when you would use the median instead of the mean?

Answer 94

(change just the top value). 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 the same group the next week, but one of them just got back from the casino and the dist 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 this time? 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 95

What does SHIFT and SCALE mean?

Answer 95

Shift is when you add or subtract, scale is when you multiply

Question 96

Think of the minimum value, the mean and the standard deviation, what is impacted by shifting (adding a constant)?

Answer 96

adding a value shifts the entire histogram to the right, so the min and the mean will increase by that amount, BUT THE SD WILL NOT CHANGE.

Question 97

Think of the minimum value, the median and the IQR, which is impacted by shifting (adding a constant)?

Answer 97

adding a value shifts the entire histogram to the right, so the min and the median will increase by that amount, BUT THE IQR WILL NOT CHANGE.

Question 98

If a distribution is skewed right, what will be greater, the mean or median? WHY?

Answer 98

Mean. The mean moves further to the right to keep balance.

Question 99

How does multiplying by a constant impact the summary statistics of a data set? (or random variable)

Answer 99

It is SCALED. Both center and spread are effected. They all (mean, median, IQR, SD, range) get multiplied by three. (BE CAREFUL, remember the variance is the SD squared, so the variance gets multiplied by 9).

Question 100

Which is more sensitive to outliers and skewed? Mean, median. Sd or IQR?

Answer 100

Mean and SD are most influenced by outliers. median and IQR are RESISTANT, RESILIENT, ROBUST!!

Question 101

are there any normal samples?

Answer 101

no, nothing is normal, just normalish. The only normal thing is the model we use.

Question 102

Which calculator function gives you a z score?

Answer 102

invnorm(%ile)

Question 103

which calculator function gives you a percent?

Answer 103

normcdf(Z left, Z right)