AP Statistics Unit 1

Quantitative

Data in the form of numbers: measurements, counts, scores, etc.

Qualitative (Categorical)

Data in the form of words and can be put into categories.

2 way table

when there are 2 categorical variables being evaluated. ex: food vs. bev.

Marginal Distribution

row or column totals

Conditional Distribution

the totals of a specific variable.

Pie Chart

data values organized by category. a chart that shows the relationship of a part to a whole. the percent of data is represented by a proportional "slice"

Bar graph

data values organized by category. a graph is organized by category on the x-axis and frequency on the y-axis.

segmented bar graph

shows the distribution of each category, expressed in percents, as bars stacked on top of each other. each bar reaches a height of 100%.

Mosaic plots

shows relative cumalitive frequency, and also the proportion in each independent category. (the fatter a bar is the more of a variable it has)

dot plots

a scaled x-axis with dots representing data values above the appropriate number.

stem plot.

needs to have all ranged numbers for the stem even if not in the data. also needs to have a key. ex: 30|8=308.

when do you split the stem?

when there are too many data values that are also varied.

histogram

visual representation of a frequency distribution. bars touch.

SOCS

Shape, Outlier, Center, Spread

Skewed left

it peaks on larger values, and looks like a wave. the median>mean.

skewed right.

it tails out to the right. it peaks near the start. it looks like a hill. mean>median.

normal

symmetric, peak is at center.

uniform

the graph looks the same all the way through; consistent. it means the values are evenly distributed.

bimodal

2 peaks on the graph.

trimodal.

3 peaks on the graph.

upper outlier

Q3+1.5(IQR)

Lower outlier

Q1-1.5(IQR)

mean

(all the data values added up)/ the number of how many data values there are. Σx/n.

median

the middle number when all data values are ordered. if a value ends in .5 average the value of the numbers it sandwiches. formula: (the numbers of how many values there are plus one)/2. (n+1)/2.

example: 3.5. average the third and fourth value.

mode

The number that appears most frequently in a data set.

standard deviation

how far away the values in a data set typically are from the average.

range

max-min

IQR

Q3-Q1

5 number summary

min, Q1, median, Q3, max

sample standard deviation.

square root of (sigma * (x-average)^2)/the number of numbers minus 1. s= √[Σ(x - x̄)² / (n-1)]

population standard deviation

square root of (sigma (x-mean)^2)/number of numbers. : σ = ∑ (X - μ)² / N

population variance

σ²=Σ(x-μ)²/N. sigma(x-mean)^2/number of numbers.

Sample Variance

s² = Σ ( x - x̄ )² / ( n - 1 ).) sigma(x-mean)^2)/number of numbers minus 1.

property of nonresistance (not resistant to outliers)

mean, range, standard deviation

property of resistance (resistant to outliers)

median, IQR

box plots

outliers are astericks. first dot is minimum, first line is q1, second is the median, third is q3, the last dot is the max. each part represents 25%.

box plot skew

if the box is closer to 0 its skewed right. if its more outward it's skewed left.

center

use median

spread

use IQR

skewed right on stem plot

looks like cliff.

skew left on stem plot

looks like tsunami.

statistic

measure that represents sample

parameter

measure that represents population

stemplot vs box plot

stemplot shows values and peaks. box plots dont.

weighted mean formula

(∑xᵢfᵢ) / (∑fᵢ). it means sigma of all the data values times their frequency, divided by all the frequency values added up.

weight standard deviation formula

√((∑fᵢ(x-μ)^2/ (∑fᵢ)). it means the square root of the sigma of a frequency of a value multiplied by the (value-the weighted average)^2 over sigma of the frequencies.

weighted standard deviation

measures the spread of a dataset where individual data points have different frequencies (the number of times they appear), assigning a higher weight to more frequent values.

weighted mean

an average that gives more importance (weight) to some values than others, due to varying frequency (number of times a value appears).

sigma

it means it applies to all the numbers in the data set.

how to find Q1

find the median, and then find the median of the bottom half values.

how to find Q3

find the median, and then find the median of the top half values.