Lecutre 3 & 4 - Visual & Numerical Data Summaries

bar plot, what and pros and what thing u get from graph

how: count number obsv per category and make bar w correspond height

pro: displays frequency of each category/level of categorical variables

can get “frequency tables”: record totals and category names

proportion = ? and whats the denotation per type of prop

prop = # cases in category / total # cases

prop of observed sample is p-hat (open down)

prop of pop is p, is the true proportion

How do u estimate range from a symmetric bell shaped curve

Range / 6

contingency table

variables across rows and columns,

segmented / side by side bar plot, what best for what?

segmented: best to see total numbers and proportions

side by side: best for exact numbers

mosaic plot, what can u find with

column width = total number in variable 1

area represents teh proportion of observations per variable

pro: desc relationships between 2 categorical variables

to compare prop see if var are ind, one white line diff level = enough to claim dependent

dot plot

represents each individual as dot along x axis

con: not good for large amt data, not all integer data, data has high range and sparse

histograms

pro: can answer many q’s, can smooth to see shape of dust

con: not show exact values of data, describes shape and density

symmetric and bell shaped histogram

data clustered in middle, equal number higher and lower

right skewed histogram

most data are smaller values

left skewed histogram

most data are larger values

symmetric and not bell shaped histogram

data values on one side mirror the other

mode, types of modes

mode = hump in graph

unimodal = 1 peak

bimodal = 2 peaks

multimodal = 3+ peaks

uniform = no hump/mode, all bars approx same height

measures of central tendency desc

summarizes data, acknowledges that each data pt may be diff but have a “center” to represent them all together

mean

numerical average value =

median

middle value when data is arranged smallest to largest

• n is even → 2 middles, so median is avg of n/2 and (n/2) + 1

• n is odd → (n+1)/2

which do u choose between mean and median

choose the one that best represents center/typical values in data set

histograms when is mean=<> median

• symmetric, mean=median

• right skew, mean>median

• left skew, mean<median

spread/variability define

describes how tight/loose the observations in data set are clustered around the measure of central tendency

how to determine outliers

more than upper fence = Q3 + 1.5 * IQR

or

less than lower fence = Q1 - 1.5 * IQR

range = , limitations

maximum value = minimum value, limitations are that it only uses 2 values to describe variation and doesnt always describe smth well

IQR = , how to find each bit

Q3 - Q1, Q1 is median of lower ½ of data, Q3 is median of upper ½ of data

departures from mean, implications, prob and sol

• distance of the mean from each observation

• larger deviations = more variable data

• problems: 1. sum of dev^n is always 0, 2. sum of squares always inc w inc obsv

• soln: 1. sum of squares 2. divide SoS by n to find mean squared deviation

population variance = , why not use much?

bc is squared

sample variance = , why not use much?

bc is squared

pop standard deviation =

sample standard deviation =

wording for stdev

the variables of the population in our sample are roughly stdev away from the mean variable of xhat on average

what does stdev do

sqrt of variance, describes how close data are to the mean, if s=0 then every data pt is same value

how are stdev and mean related for symmetric bell shaped graphs

• mean +-1 stdev = 68% of data

• mean +-2 stdev = 95% of data

• mean +-3 stdev = 99.7% of data

notation for parameter, mean variance, stdev, pop

notation for statistic, mean variance, stdev, pop

which ones are robust to outliers?

median, IQR

which ones are sensitive to outliers?

mean, stdev, range