AP stats: unit 1

categorical data

Data that consists of names, labels, or other nonnumerical values (averages are meaningless)

examples: grade, fav season, birth month

What is statistics?

A way of reasoning, along with a collection of tools and methods to help us understand the world

It’s the science of collecting, organizing, analyzing and interpreting data.

quantitative data

numerical data (averages give some sort of information)

examples: # of people, age, time, height

frequency table

includes category and frequency (amount)

relative frequency

includes category, frequency (amount), and relative frequency (%)

Ways to represent categorical data

pie chart, bar chart, dot plot

Rules for bar chart

Label your axes: variable name on horizontal, frequency on vertical

Scale axes: start scaling vertical axis at 0 and go up in equal increments until you =/< maximum frequency

Draw bars: make them equal in width and leave gaps

Types of quantitative data

discrete (whole numbers with gaps) and continuous (no gaps, can be decimal)

dot plot advantages and disadvantages (quantitative data

advantages: shows every individual value, easy to see shape of distribution

disadvantages: bad for large amts

Ways to represent quantitative variables

dot plot, stem plot, histogram

stem plot advantages and disadvantages

shows every individual value in the data set, easy to see distribution shape

disadvantages: difficult to make for large data sets

histogram advantages and disadvantages

advantages: good for large data sets, easy to see distribution shape

disadvantages: doesn't show every individual value

cumulative frequency

the sum of the frequencies for that class and all previous classes

factors to comment on to describe a quantitative variable

shape, center, variability, unusual features

IQR range

Q3-Q1 where Q1 is in between the min and median, and Q3 is between max and median

Formula for outliers

Lower fence: Q1 - 1.5 x IQR

Upper fence: Q3 + 1.5 x IQR

If it goes beyond these boundaries, it’s an outlier

Range

highest value - lowest value

Variance

standard deviation squared

skewed left

mean is less than median

skewed right

mean is greater than median

standard deviation

the square root of the variance (always less than variance when variance => 1)

if you add a constant to add values, SD remains the same

ways to describe distribution

shape, center, spread, variability

shapes of graphs

Uniform (roughly the same across all points)
Symmetric (no skew)
Skewed right (more low values)
Skewed left (more high values)
unimodal (one spot where data raises forming a lump)
bimodal (two spots where data raises forming a lump)

center

median and mean

unusual features

outliers, gaps, clusters

Variability

IQR, range, standard deviation, variance

Box plot/five number summary

minimum, Q1, median, Q3, maximum

Histogram

a bar graph depicting a frequency distribution (larger, more inspecific data points)

z-score

how many SD away from the mean;

value given > mean = positive
value given < mean = negative

Percentile

amount below or equal to the point

if you are in 99th percentile, you're the top 1%

number of values before & including value / total data

68-95-99.7 rule

in a normal model, about 68% of values fall within 1 standard deviation of the mean, about 95% fall within 2 standard deviations of the mean, and about 99.7% fall within 3 standard deviations of the mean

Z-Score Chart

use if you can't find % with the rule

working backwards

find closest value on z-score chart and solve for x

Adding data

If adding amount: range, SD and variance stays the same but mean changes

If adding percentage: change all by multiplying by 1.x but variance is still just SD²

Finding median and IQR with cumulative frequency chart

Point where cumulative proportion is 0.5 = median

Q1 is between median and lowest, Q3 is between median and highest → find both then use Q3 - Q1 to find IQR