AP Stat Ch 1

Question 0

Available data

Answer 0

The data that were produced in the past for some other purpose but that may help answer a present question

Question 1

Statistics

Answer 1

The science of collecting, analyzing, and drawing conclusions from data

Question 2

Observational study

Answer 2

In an observational study, we observe individuals and measure variables of interest but do not attempt to influence the responses

Question 3

Experiment

Answer 3

In an experiment, we deliberately do something to individuals in order to observe their responses

Question 4

Individuals

Answer 4

Individuals are the objects described by a set of data. Individuals may be people, but they may also be animals or things. Do not get individuals confused with the population

Question 5

Population

Answer 5

The population of interest is the entire collection of individuals or objects about which information is desired

Question 6

Variable

Answer 6

Any characteristic of an individual whose value may change from one individual to another.
Ex. Hair color, height, brand of car, gpa

Question 7

Categorical variable

Answer 7

An individual into one of several groups or catergories.
Ex. Hair color, brand of car
USUALLY WORDS AS OPTIONS

Question 8

Quantitative

Answer 8

Numerical data. Takes numerical values for which arithmetic operations such as adding and averaging make sense.

Question 9

Categorical vs quantitative variables

Answer 9

Categorical is w words whereas quantitative is with numbers–can do operations to them

Question 10

Census

Answer 10

When you study an entire population, it is called a census

Question 11

Sample

Answer 11

A sample is a subset of the Population, selected for study in some prescribed manner

Question 12

Descriptive statistics

Answer 12

The branch of statistics that includes methods for organizing and summarizing data

Question 13

Inferential statistics

Answer 13

The branch of statistics that involves generalizing about a population based on information from a sample of that population.

Question 14

Statistical inference

Answer 14

The process of drawing these generalizations about inferential statistics

Question 15

Distribution of a variable

Answer 15

Tells us what values the variable takes and how often it takes these values

Question 16

Discrete data

Answer 16

Quantitative data is discrete if the possible values are isolated points on the number line.

Shoe size, number of birthdays. Count them. Whole numbers.

Question 17

Continuous data

Answer 17

Numerical data is continuous if the possible values form an entire interval on the number line

Foot length, age

Question 18

Discrete vs continuous variables

Answer 18

Measure continuous, count discrete

Question 19

Types of variables

Answer 19

First decide if Categorical or quantitative.
If catergorical, then it is words– hair color, fav color, fav president
If quantitative then it is numbers – age, number siblings

If quantitative, then discrete or continuous
Discrete if u can count it, continuous if u measure it.
Discrete is number of pages, continuous is length of an inseam

Question 20

Are the following quantitative (continuous or discrete) or caterogircal: 
Length of pen
Color of pants
Subject of book
Type of pen
Number of pockets
Number of pages
Number of pens in a box
Length of an inseam
Area of a page

Answer 20

Length of pen– quantitative, continuous
Color of pants– caterogircal
Subject of book– cateofgircal
Type of pen– cateorgircal
Number of pockets– quantitative, discrete
Number of pages– quantitative, discrete
Number of pens in a box – quantitative, discrete
Length of inseam– quantitative, continuous
Area of a page– quantitative, continuous

Question 21

Frequency table

Answer 21

For caterogircal data, make a frequency table – displays the possible catergories and either the count or the present of individuals who fall in each category

Question 22

Frequency

Answer 22

Count– # of items in that group

Question 23

Relative frequency

Answer 23

Percent of your thing. If you have 2 and there are 11 total, relative frequency = 2/11

Question 24

Ways to display caterogircal data

Answer 24

Bar graphs and relative frequency bar graphs Pie charts and segments bad charts Two way table

Question 25

Bar graphs and relative frequency bar graphs

Answer 25

Label variables and scales The bars should be the same width and not touching each other The order of the categories doesn't matter Relative frequency bar charts make it easier to compare multiple distributions, especially when the sample sizes are different

Question 26

Pie charts and segmented bar charts

Answer 26

Label variables and categories Pie charts are easier to construct with a computer spreadsheet program or stat software Pie charts help us visually see what part of the whole each group forms Segmented bar charts are basically rectangular pie charts, each bar is a whole, divide each bar proportionally into segments corresponding to the percentage in each group Segmented bar charts make it easier to compare distributions

Question 27

AP exam common error with charts

Answer 27

BE SURE TO LABEL GRAPHS!!!

Question 28

Suppose I wanted to compare AP stat scores for tenth, eleventh, and twelfth graders. Which type of graph would be the best?

Answer 28

Segmented bar chart | Three bars, one with tenth, one with eleventh, one with twelfth

Question 29

Two way table

Answer 29

A table with two categorical variables

Question 30

Marginal distribution

Answer 30

Distributions of categorical data that appear at the right and bottom margins of a two way table. They help us to look at the distribution of each variable separately

Question 31

Conditional distributions

Answer 31

Caterogiral distrivutions inside a two way table that deals w a specific number inside the table

Question 32

How many total conditional distributions are there?

Answer 32

Rows + columns

Question 33

Simpson's paradox

Answer 33

An association between two variables that holds for each individual value of a third variable can be changed or even reversed when the data for all values of the third variable are combined. This reversal is called Simpson's paradox. Therefore You must be careful when data from several groups are combined to form a single group! Data that suggests one conclusion when aggregated and a different conclusion when presented in subcategories

Question 34

Lurking variables

Answer 34

With Simpson's paradox Sometimes the relationship between two variables is influenced by other variables that we did not measure or even think about! Because the variables are lurking in the background, we call them lurking variables. They are not among the explanatory or response variables in a study, but they may influence the interpretation of the relationship among these variables.

Question 35

Conclusions from Simpson's paradox

Answer 35

It is caused by a combination of a lurking variable and data from unequal sized groups being combined into a single data set. The unequal group sizes, in the prescense of a lurking variable, can weight the results incorrectly. This can lead to seriously flawed conclusions. The obvious way to prevent it is to not combine data sets of different sizes from diverse sources! A great deal of care has to be taken when combining small data sets into a larger one. Sometimes Conclusions from large data sets are the opposite of conclusions from smaller ones. Conclusions from large set are usually wrong!

Question 36

Dotplot

Answer 36

A simple way to display quantitative data when the set is reasonably small

Question 37

How to construct a dotplot

Answer 37

Label your axis (horizontal line) with the variable and title your graph Scale the axis based on the values of the variable Mark a dot above the number on the horizontal axis corresponding to each data value. Stack multiple dots vertically

Question 38

Stem and leaf plot

Answer 38

Another way to display a relatively small numerical data set. Often the values of the variable are too spread out to make a dotplot, so this is a better option. Stem is the first part of the number and leaf is last digit

Question 39

How to construct a stem plot

Answer 39

Separate each observation into a set consisting of all but the rightmost digit and a leaf, the final digit. Write the stems vertically in increasing order from top to bottom, and draw a vertical line to the right of the stems. Write each leaf to the right of its stem. Numbers to the left of the line are the stems and to the right are the leaves. MUST INCLUDE A KEY W UNITS LEAVES MUST BE IN SINGLE DIGITS, NO COMMAS it is best if leaves are in numerical order

Question 40

Back to back stemplots

Answer 40

Useful for comparing distributions Example is comparing female and male weights Have stem in the middle and leaves on both sides with male above one side and female above the other

Question 41

Split stemplot

Answer 41

When a data set is very compact, it is often useful to split stems to stretch the display to investigate the shape. Whenever you split stems, be sure that each stem is assigned an equal number of possible leaf digits. When given data all between 96 and 99, make stems 96,96,97,97,98,98,99,99 and have the top be 0-4 for leaves and bottom be 5-9

Question 42

What to do when data is spread out for stem and leaf plot

Answer 42

Truncate or round the data to shrink the display | Change 10.53 to 11

Question 43

Describing a distribution

Answer 43

SHAPE, CENTER, AND SPREAD

Question 44

Shape

Answer 44

Symmetric, skewed right, or skewed left Unimodal if one peak, bimodal if two peaks Uniform if a plateau, get same values

Question 45

Outliers

Answer 45

Data values that fall outside the overall pattern of the rest of the distribution. Q3 + 1.5IQR

Question 46

Clusters

Answer 46

Isolated groups of points of points

Question 47

Gaps

Answer 47

Large spaces between points

Question 48

Symmetric

Answer 48

If the right and left sides of the historgram are approximately mirror images of each other

Question 49

Skewed

Answer 49

The thinner ends of a distribution are called the tails. If one tail stretches out further than the other, the historgram is said to be skewed to the side of the longer tail

Question 50

Histogram

Answer 50

Used to display larger data sets for quantitative data

Question 51

Discrete histogram vs continuous histogram

Answer 51

In discrete historgrams, make the bars over the center of the number on the X-axis. In continuous histograms, make classes where the bars fall between. For example, make groups of 5 and have on the left edge 40, right edge 45 and then 50 and then 55.

Question 52

How to make histograms

Answer 52

Label axis and scales Bars should touch Y axis is frequency or relative frequency X axis is variable

Question 53

Relative frequency histograms

Answer 53

Same as regular histogram, but have relative frequency (percent of total) rather than frequency (number of observations) on the vertical axis. Relative frequency histograms are more useful because you can compare two distributions easier

Question 54

Histograms vs bar graphs

Answer 54

Histograms uses QUANTITATIVE variables while bar graphs use CATEGORICAL data. Histograms don't have spaces between bars, bar graphs have spaces

Question 55

Continuous histograms

Answer 55

``` Make classes of the same length that never overlap Divide the range of the data into classes of equal width. Count the number of observations in each class Five classes is a good minimum. Too few will give a skyscraper graph and too many will give a pancake graph. Label and scale your axes If an observation falls on a boundary, put the value into the upper class. ```

Question 56

Ogive

Answer 56

Culumative relative frequency graph | Relative culm frequency is percentile

Question 57

Measuring the center of a data set

Answer 57

Look at the mean and the median

Question 58

Population mean

Answer 58

Greek letter mu (u with long stem) | The arithmetic average of all values in the entire population

Question 59

Sample mean

Answer 59

X with a bar above it. Since we rarely study the entire population, estimate population mean with the sample mean = sum of all values / number of values

Question 60

Median

Answer 60

The middle score | To find which value is the middle score, put all the data in order

Question 61

Mode

Answer 61

Most frequency observation. Not a useful measure of center.

Question 62

Resistant measure

Answer 62

Measure not affected by outliers

Question 63

Are median and mean resistant?

Answer 63

Median is resistant--not affected by outliers so it is better for a skewed data set Mean is not resistant--affected by outliers, as outliers affect arithmetic average.

Question 64

When to use mean and when to use median

Answer 64

Use median with all data | Mean with symmetrical data since mean is not resistant and median is

Question 65

Skewed right vs skewed left

Answer 65

Skewed left is when the tail is to the left. Median> mean Lower values that push the graph to the left. Bell curve on right. Tail on left. Skewed right is when the tail is to the right Mean>median Bell curve on the left.

Question 66

Mean vs median in skewed data

Answer 66

Skewed left: Median> mean Skewed right: Mean> median Symmetric: Mean roughly equal to median

Question 67

Range

Answer 67

Full spread of data by simply finding the difference between the largest and the smallest observation. ONE NUMBER MAX-MIN BUT it is not resistant. Outliers heavily influence the range

Question 68

How to measure spread

Answer 68

Range for roughly symmetric data without outliers. | IQR when skewed or have outliers

Question 69

Inter-Quartile Range

Answer 69

A resistant measure of spread. It is the distance between the first and third quartiles. The range of the middle half of the data. IQR=Q3-Q1

Question 70

Quartiles

Answer 70

Q1 is first quartile--the point that divides the lowest 25% of the data from the upper 75% Q2 is the median Q3 is the third quartile--the point that divides the lowest 75% of the data from the upper 25%

Question 71

How to find quartiles

Answer 71

Get data in order. Find median. Median is Q2 Half the data above the median is Q3 and half the data below the median is Q1 In that data above the median, take that median. That value is Q3. Do the same for the data below the median and get Q1

Question 72

Shape center spread summary

Answer 72

Shape: Skewed (direction) or symmetric Unimodal or bimodal Center: Mean or median Spread: IQR, range, standard deviation

Question 73

Five number summary

Answer 73

(MIN,Q1,MED,Q3,MAX)

Question 74

Box plot

Answer 74

A graph of the five number summary. Easy to make and clearly shows center and spread of the distribution. Skewed toward the side with the longer box. Useful to compare multiple distributions -- side by side boxplots and are usually drawn vertically

Question 75

Drawing a box plot

Answer 75

Central box spans the quartiles Q1 and Q3 A line in the box marks the Median, M Lines extend from the box out to the smallest and largest observations. Width of the box = IQR label axes and scale

Question 76

Modified boxplot

Answer 76

Specifically identifies outliers, in addition to median and quartiles. Regular boxplot connects outliers.

Question 77

Variance

Answer 77

Averaged squared deviation of the observations from the mean S squared

Question 78

Deviation

Answer 78

The deviation of an observation is its distance from the mean (x-x bar). The mean is the point that makes the sum of the deviations=0. We square the deviations to make negatives positives.

Question 79

Population standard deviation

Answer 79

Greek letter looking like the letter "o' Standard deviation of all the values in the entire population. Typical deviation from the mean or the average distance form the average = SQRT (sum of (x-mu)^2 / n)

Question 80

Population variance

Answer 80

Square of the population standard deviation | Greek letter looking like "o" squared

Question 81

Sample standard deviation

Answer 81

Represented by s Since we rarely study entire populations, use this. Your distance from the center or your average distance from the average. Approximates the average, or typical deviation = SQRT ( sum of (x-x bar)^2 / (n-1))

Question 82

Sample variance

Answer 82

Square of the sample standard deviation. | S squared

Question 83

Why do we divide by n-1 when calculating the sample standard deviation

Answer 83

Some error between x bar and mu, so this helps to accounts for this.

Question 84

When to use sample and when use population

Answer 84

Use sample unless told otherwise

Question 85

When to use sample standard deviation

Answer 85

When talking about mean, as this measures spread about the mean.

Question 86

When does s=0

Answer 86

When there is no spread. All observations have same value. Otherwise, s>0 As observations are more spread out about their mean, s is larger.

Question 87

Is s resistant?

Answer 87

No because like the mean | Strong skewness or outliers can make S very large

Question 88

5 number summary

Answer 88

Usually better than the mean and standard deviation for describing a skewed distribution or a distribution with strong outliers Use the mean and s when with reasonably symmetric disturbition free of outliers.

Question 89

Transformations to lists

Answer 89

Shape never changes. Center always changes -- when multiplying each observation by b, multiply both mean and median by b. Adding same number a adds a to mean and median Spread stays the same when adding same amount to each but increases if multiply each data point by something. When milt by b, spread is multiplied by b.