AP STATS

Categorical Data

Describe categories or labels

NOT numbers you calculate with

Examples:

Eye color (brown, blue, green)

Gender

Favorite subject

👉 Think: "groups"

Quantitative Data

Take on numeric values

You can do math with them

Examples:

Height (in inches)

Test scores

Number of siblings

👉 Think: "numbers you can calculate with"

Individuals

the objects/people you're studying

Two-way Tables

A table of counts describing two categorical variables

Marginal Distribution

a summary that shows the totals for one variable in a table, using the row or column total

Stemplot advantages and disadvantages

Advantages: see exact values

Disadvantages: overwhelming for large datasets

Histogram advantages/disadvantages

Advantages:

Good for large data sets

Helps focus on the general shape of the data

Disadvantages:

Individual data values are not visible (lost)

Distribution shape affected by change in bin width

Frequency

the number of times something occurs

relative frequency

how often something happens out of the total (fraction/percentage)

z-score

a measure of how many standard deviations a data point is above/below the mean

formula: data point-mean/SD

Standarization

a point location in the distribution depends on both distance from the center and the distributions spread of variation

Positive Z-score

number of standard deviations above the mean

negative z-score

number of standard deviations below the mean

adding or subtracting same number to every data

center: increases or decreases by that number

spread: stays the same

shape: stays the same

multiplying or dividing the same number to every data value

center: multiplies/divides by that amount

spread: multiplies/divides by that amount

shape: remains the same

Describe the distribution

CSOCS

Context-what variables is being measured

Shape-right/left skew, symmetric, modes

Outliers- unusual point

Center- Mean,median,general center

Spread- Range,IQR,SD

UNIMODAL

one peak

BIMODAL

two peaks

RIGHT SKEW

mean > median

SYMMETRIC

mean = median

LEFT SKEW

mean < median

RANGE

MAX-MIN

IQR

Q3-Q1, the middle 50% of the data

OUTLIERS

Numbers that are much greater or much less than the other numbers in the set

Upper Limit: Q3 + 1.5 x IQR

Lower Limit: Q1 - 1.5 x 1QR