AP Statistics Unit 1

What do you need to remember when plotting?

Title

Tick, Tick (x and y axis)

Label, label, label (x and y axis, key for stem-and-leaf plot)

relative frequency

frequency / total

Describing Quantitative Data: C S(4) O C S

Context

Shape: Skewed left/skewed right/symmetric, uniform, unimodal/bimodal, gaps

Outliers: Unusual data points

Center: Mean (average) or Median (middle value)

Spread: Range, IQR (Q3 – Q1), Standard Deviation

Left-skewed looks like ____, median ____ mean

Right-skewed looks like ____, median _____ mean

How to describe the shape of stemplots? ______

Tail on the left, median > mean

Tail on the right, median < mean

Rotate so stems are on the bottom

3 Measures of center

mean, median, general center

Mean is denoted by ___ for ____ or _____ for ______

μ for population; x̄ for sample

Median position formula

n+1 / 2

3 Measures of spread

range, IQR, standard deviation

Standard deviation: typical ____ from the ____

What’s the formula? ___

Find the distances from mean for each point, ____ them, ___ them up, divide by _____, and take the ____

distance, mean

square, add, n-1, sq root

Range formula:____ Range is a ____

max-min

number

IQR Formula

Q3-Q1

Choosing appropriate measures of center and spread

If the data is fairly symmetric, use the ____ and _____.

If the data is skewed or outliers are present, use the ______ and _____ instead.

mean, standard deviation

median, IQR

Formulas for outlier boundaries:
Upper limit: ____

Lower limit: ____

Q3 + 1.5xIQR

Q1 - 1.5xIQR

6 Components of a box plot

min, Q1, median, Q3, max, outliers

CSOCS for boxplot

C: context

S: Skew (not modes)

O: dots

C: median

S: IQR

When asked to compare distributions for dotplots, stemplots, histograms, and boxplots

1. use _____

2. use _____ language and _____ for each feature

csocs

comparative (eg. less than, greater than, similar), NUMBERS

Linear transformations: adding or multiplying by a constant. Did these change?

SOCS

Addition only affects center and five number summary positions

multiplication affects center and spread, five number summary positions

Quantitative data: Data that is ______. The values have an inherent _____. See if it makes sense to ____ it

Categorical data: Data where values are categories or group labels, which often ____ have an inherent order

numerical, order, average

don’t

6 ways to graph quantitative data

Dotplots

Histograms

Stemplots

Boxplots

ogive (cumulative relative frequency graph)

timeplot

4 ways to graph categorical data

stacked bar graph

pie chart

bar graph

mosaic plot

3 parts of Describing Categorical Data

Context, relative frequency (%s), modes

Ogive: cumulative relative frequency graph

cumulative relative frequency on y axis

• can find Q1, med, Q3 by finding 25%, 50%, and 75% on y-axis

Timeplot

time is on x-axis

collecting data from sample —>

collecting data from population —>

statistic

parameter

uniform distribution

variance

standard deviation squared

how to draw histogram from boxplot

do 4 equal area rectangles from the quartiles (since each contains 25% of data) then split them up into equal sized bins

don’t forget to do this when making boxplot

find outliers

how to show higher concentration of data in histogram, dotpot, boxplot, ogive, stemplot

taller bins

taller bins

skinnier boxes/quartiles

steeper slope

more leafs