Ch. 2 Materials

proportion

x number of people who responded a certain way/total (AKA relative frequency)

symbols for proportion

sample: p-hat; population: p

two-way table purpose

to investigate relationship between 2 categorical variables

outlier

observed value that is noticeably distinct from other values in a dataset; outlier if smaller than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR)

mean vs. median when data is: skewed to the right, skewed to the left, symmetric & bell-shaped

mean > median, mean < median, m = median

mean caluclation & symbol

sum of all data values/number of all data values, symbolized by x bar for sample (statistic) and mu for population (proportion)

median

middle entry (odd) or average of 2 middle entries (even)

resistance

related to the impact of outliers on a statistic

standard deviation definition & symbols

measures how much variability is in the data (larger values = more spread out data), s for sample and sigma for population

if distribution is symmetrical and bell-shaped, about what percent of data should fall within 2 standard deviations of the mean? (mean - 2 to mean + 2)

95%

z-score

how many standard deviations the value is from the mean: (x - mean)/s or (x - mu)/sigma

Pth percentile

value of a quantitative variable that is greater than P% of the data

Q1, Q2, Q3

first quartile = 25th percentile, second quartile = 50th percentile = median, third quartile = 75th percentile

range & interquartile range

max - min, Q3 - Q1

5 number summary

minimum, Q1, median, Q3, maximum

boxplots include:

appropriate numerical scale, box from Q1 → Q3, line at median, line from each quartile to most extreme data that isn’t an outlier, plotted outliers

side-by-side graphs

facilitate comparison of distributions, includes graph for quantitative variable for each group in the categorical variable

scatterplots

graphs of relationship between two quantitative variables (explanatory variable on x-axis, response variable on y-axis)

correlation

measure of strength and direction of linear association, sample = r and population = rho

correlation key things to note

always between -1 & 1, sign indicates direction of association (positive or negative), if closer to 1 or -1 it’s stronger correlation, no units, does not imply causation, just because it’s near 0 doesn’t mean variables aren’t associated, can be heavily influenced by outliers

histogram vs. box plot

histograms are for quantitative/numeric data where we are choosing our bins

mode

the value with the highest frequency OR the bin with the highest frequency when it’s a histogram