stats unit 1 chapter 1

individual

person or object described in the data set

variable

- any characteristic, number, or quantity that can be measured or counted
- types: categorical and quantitative

categorical variable

- takes on names or labels
- places individual into groups
- ex: eye color

quantitative variable

- takes on numeric values
- types: discrete and continuous
- ex: class size

discrete variable

- fixed set of possible values
- ONLY WHOLE NUMBERS

continuous variable

- any value in an interval on the number line
- decimals

bar graph

- each bar represents frequency or relative frequency for each category
- used to compare discrete or categorical variables (counts)
- bars don't touch

side-by-side bar graph

pie chart

segmented bar graph

stack up the bars to make 100%

mosaic plot

segmented bar graph where the width of the bars is proportional to group size

dot plot

association

if knowing the value of one variable helps us to predict the value of the other variable

descriptive statistics

describing something

inferential statistics

- drawing conclusions that go beyond the data at hand
- using sample data to make an inference about population

misleading graphs

- vertical axis should start at 0
- be wary of pictographs

marginal relative frequency

- totals
- ex: 53/121

joint relative frequency

- in the table and total
- ex: 7/121

conditional relative frequency

- within the table
- ex: 7/53

symmetric

- right side approximately mirrors left side
- mean ≈ median
- use mean and standard deviation to describe

skewed to the right

- right side of the graph is longer
- mean > median
- use median to describe

skewed to the left

- left side of the graph is longer
- mean < median
- use median to describe

describing distributions

- include context
- shape: skewness, symmetric, bimodal
- outliers
- center: mean (symmetric), median (skewed/outlier)
- variability: how spread out data is

stem plots

turn stemplot to the side and you can read it like a dot plot

histograms

- vertical axis shows the frequency or relative frequency
- use percents or proportions on vertical axis
- bars touch

median

- midpoint
- resistant to outliers
- used to explain skewness and outliers

mean

- average
- affected by outliers
- used to explain symmetry

range

- maximum - minimum
- not a resistant measure of variability

standard deviation

- distance of values from the mean
- larger value indicate greater variability
- affected by outliers (nonresistant)
- always greater than or equal to 0
- "n" is how many terms there are

sample variance

standard deviation without the square root

measures of center

- mean
- median

measures of variability

- range
- standard deviation
- "the context typically varies by SD from the mean of x̄"

interquartile range

Q3-Q1

box plots

outliers are a dot separate from the box plot

first quartile

median of values left of the median in the ordered list

third quartile

median of values right of the median in the ordered list

five number summary

minimum, Q1, median (Q2), Q3, maximum

low

___ outliers < Q1 - 1.5IQR

high

___ outliers > Q3 + 1.5IQR

outliers

influences mean, range, and standard deviation

comparing distributions

- shape
- outlier (1.5IQR rule)
- center (mean, median)
- variability (standard deviation, IQR, range)