1.1 AP STATS VOCAB

Statistics

the science and art of collecting, analyzing, and drawing conclusions from data

Indiviudal

an object that can be described in a set of data, individuals can be ppl, animals or things

Ex: If a survey collects the SAT scores of high school seniors, the individuals are the students.

Variable

An attribute that can take different values for different individuals

Ex: If a survey collects the SAT scores of high school seniors, the variable are SAT Scores

Categorical Variable

assigns labels that place each individual into a particular group called a category

EX: If I am collecting data on what people’s favorite cuisine; Categorical Variables would be the different types of cuisines like: Indian, Thai, Italian, Mexican

Quantitative Variable

Takes number values that are quantities — counts of measurements

Ex: If a survey collects the SAT scores of high school seniors, their scores are the quantitative variable

Other examples are: heights, weights, age

ASK YOURSELF: Can i take the mean; if you can it’s probably quantitative

Discrete Variable

A quantitative variable that takes a fixed set of possible values with gaps btwn them

Basically can be countable

Ex: Number of siblings, How many langauges one can speak

Continuous Variable

A quantitative variable that can take any value in an interval on the number line

(these things can be measured for example)

Ex: Heights, time, temperature

Distribution

The distribution of a variable tells us what values the variable takes and how often it takes those values

Basically you use SOCV + context when asking to describe distribution

Ex: Example: Test Scores

Suppose 10 students take a quiz, and the scores are:
70, 70, 75, 80, 80, 80, 85, 90, 95, 100

• Distribution → shows how the scores are spread:

  • 70 appears 2 times

  • 75 appears 1 time

  • 80 appears 3 times

  • 85 appears 1 time

  • 90 appears 1 time

  • 95 appears 1 time

  • 100 appears 1 time

If you graphed this with a histogram or dotplot, the shape of the graph is the distribution

Frequency Table

shows the # of individuals having each value

Basically this is like a summary of the raw data; example; how many ap classes students at fhs take

Raw Data: 1,3,5,5,6,2,3,4,5,7

Frequency might be like

1: 1

2: 1

3: 2

4: 1

5: 3

6: 1

7: 1

REMEMBER FREQUENCY is not DATA but more like summary

Relative Frequency Table

shows proportion or percent of individuals having each value

Basically like Frequency Table js in proportion or percent

Ex: Raw Data: 1,3,5,5,6,2,3,4,5,7

Frequency might be like

1: 1

2: 1

3: 2

4: 1

5: 3

6: 1

7: 1

Relative frequency:

1/10; 0.1, 10% for 1 ap

1/10; 0.1; 10% for 1 ap

and like yk u get the gist

Bar Graph

shows each category as a bar. the heights of the bars show the category frequencies or relative frequencies

Remember: NOT THE SAME AS A HISTOGRAM; Bar for Categorical Data like cuisines while histo for quantitative data

For bar graph; bars DONT touch cuz different categories but they do for histo

Pie chart

shows each category as a slice of the pie. The areas of slices are proportional to the category frequencies or relative frequencies

Two Way Table

Is a table of counts that summarizes data on the relationship btwn two categorical variables or some group of individuals

Ex: Favorite Cuisine vs Grade Level

Or

Male vs female and Car Type Perference

Marginal Relative Frequency

Gives the % or proportion of individuals that have a specific value for one categorical variable

Basically you only look at 1 variable; so if i was measuring grade level and cuisine; i only look at grade level or cuisine

You look at the total sections; or the MARGIN section of the table

Joint Relative Frequency

Gives the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for another categorical variable

Basically js everything out of total

Conditional Relative Frequency

Gives the % or proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable (the condition)

Basically can place a condition on row; where you divide each cell by its total

or place a condition on column where you divide each cell by its total

A side-by-side bar graph

displays the distribution of a categorical variable for each value of another categorical variable. The bars are grouped together based on one of the categorical variables and placed side by side

Essentially a two way table but like in bar graph; but both bars are next to each other

Segmented Bar graph

displays the distribution of a categorical variable as segments of a rectangle, with the area of each segment proportional to the percent of individuals in the corresponding category

Ex: Basically a side - by side bar graph; except like one of the categorical variables are all stacked on top of each other

A mosaic plot

a modified segmented bar graph in which the width of each rectangle is proportional to the number of individuals in the corresponding category

This is used when there might not be an equal amount of people surveyed for each category

Ex: if its like grade level and cuisine; but if i have a lot more freshman than juniors; i would make the freshman bar like wider

Association

There is an association btwn 2 variables if knowing the value one variable helps us predict the value of the other. If knowing the value of one variable does not help us predict the value of the other, then there is no association btwn the variables

Ex: Does grade level help predict what cusine?

Typically: Grade level: explanatory variable

Cusiine: Response variable