Ch1 - exploring data

Data Analysis

is the process of organizing/showing/summarizing/asking questions about data

individuals

objects described by a set of data

variables

any characteristic of an individual

Categorical Variable

places individuals into one of several groups of categories

• zip codes

  • 20s, 30s

• bar graphs, pie charts

can still be %

Quantitative Variable

takes numerical values for which it makes sense to find an average

• avg age of highschooler

• dot plots, stem & leaf plots, histograms

diff from %

in a scenario data can either be

categorical or quantitative

pictographs/bar graphs

visual representations of data using pictures or bars to show frequency or quantity.

• side-by side bar graphs

• segmented bar graphs

• mosaic plot

side-by side bar graphs

shows (relative) frequency proportions of quantitative data, side-by-side

• only use a count when sample sizes are the same (two classes of 24)

segmented bar graph

shows (relative) frequency proportions of quantitative data, stacked

• only use a count when sample sizes are the same (two classes of 24)

mosaic plot

shows (relative) frequency proportions of quantitative data, with areas that are proportional to the frequencies of categories.

cherrypicking

picking specific data points to show desired graph + changing scaling

Bar Graphs show

categorical data (also shown by pie charts)

• in frequency (if same sample size)

• and in relative frequency (if diff sample sizes)

frequency

for categorical data = the count (how many) of observations in each category or class

relative frequency

for categorical data = the % of observations in each category or class

Two Way Tables

show the frequency counts for each combination of categories.

• show marginal distribution

• show conditional distribution

• can show association

marginal distribution

is the distribution of values of that variable among all individuals described by the table (total)

margin

a subset of values in a larger set of data, a variable NOT value

conditional distribution

describes the values of that variable among individuals who have a specific value of another variable (probability)

association

knowing the value of one variable helps predict the value of the other.

• Since knowing the favorite core subject will help us predict favorite elective, we say there is an association between the two variables.

is proven stronger when there is a greater difference between the variables of two classes

distribution

the way in which values of a variable are spread across a range.

• All the values that the zoologist records for body temperature and how many individual bears have each value.

marginal or conditional

dotplot

display of quantitative data

each data value is shown as a dot above its location on the # line

• continuous x-axis

• consistent scale

• label units

stem & leaf plot

display of quantitative data

• the stems must be continuous + 5 min

• leaves are single digit

• include key for 1st data idem

• does not work well w big sets

if split stems, do so equally BY ONES PLACE: 0-1, 2-3, etc

Histogram

display of quantitative data

• divide range of data into classes of equal width

• Find the count (frequency) or % (relative frequency) of individuals in each class

• label & scale axes & draw histogram. adjacent bars touch unless a class contains no individuals

• GIVE KEY (,] or [,)

vocab to describe histogram

• left bound graph

• right bound graph

• skyscraper graph

• pancake graph

left bound graph

histogram whose buckets include left [left,right) not right

right bound graph

histogram whose buckets include right (left,right] not left

skyscraper graph

too few classes in histogram graph

pancake graph

too many classes in histogram graph

Histogram on calc

• List: stat, edit

• Make Histogram: 2nd, Y= (STAT PLOT)

  • press 1, turn on desired plot

• press zoom 9

• adjust window

• press graph (do not press zoom again)

press TRACE to see 5# list

5 descriptors of a graph

dont forget you SOCCS

• shape

• outliers → “appears to be”

• center → median or mean → “middle value”

• context → units

• spread → range (min-max), spread (min, max), IQR, standard deviation

describing shape

• rough symmetry

• uniform → height is roughly same for whole graph

• right-skewed/left-skewed → which dir. graph tails

AND

• unimodal → /\

• bimodal → /\/\

• multimodal

formula for sample mean

“x bar” = sum (all data items)/ # of items

Describing center

The measures that describe the center of the data 5pt)

1. the median: middle #, resistant to outliers

2. the mean: avg #, is impacted by outliers

3. Quartiles: the 25% ‘s

4. Spread; [9,24] or the range; 24

5. IQR: measures the range of the middle 50%

the median

middle # in order, resistant to outliers

the mean

avg #, is impacted by outliers

should we use mean or median

• when graph is approx symmetric: mean or standard deviation is more accurate

• when graph is skewed median/center, or IQR is more accurate bc mean is pulled to skew

Quartiles

the 25% ‘s

• 1st quartile = median of lower half

• 3rd quartile = median of upper half

(if even then include median, if odd then exclude median)

IQR

measures the range of the middle 50%

• IQR = Q3-Q1

graphically representing the center (box plot/box & whisker plot)

box plot/box & whisker plot

• box shows middle 50%

• line is median

• lines show quartiles and outliers with *

is it an outlier

an observation that falls 1.5 x IQR = outside boundary

• above Q3: Q3 + 1.5(IQR)

• below Q1: Q1 - 1.5(IQR)

if on boundary its included

standard deviation

measures the avg distance from the mean (should only be used when mean measure of center) always > or = 0

• calculated by taking square root of variaance / square root of (Sx²)

• = Sx (same units as og observations)

is not resistant - very impacted by skew + outliers bc of square (goes toward skew/outliers)

Sx = root (variance), standard deviation

variance

how spread out the data is

• (Sx²)

is not resistant - impacted by skew and outliers in the data set (more skew/outliers = greater spread)

measures of center vs variability

center: median, mean

variability: range, spread, IQR, standard deviation