Description
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Descriptive Statistics
methods for organizing and summarizing information
graphs, charts, tables * averages, vanation, percentiles
@ready
happened
"descnbe" the data
f data
1. collection 2 presentation 3. analysis 4 interpreting Don't forget about the age old question of What is the meaning of homogamy in romantic love?
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visuals
Statistics
G descnptive inferential k
confidence introval
predict, infer estimate hypothesis testing not as straight forward
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Population
the collection of all individuals or items under consideration in a stafistical study Don't forget about the age old question of What is the meaning of parameters around the design in art and design?
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pulation from which information is obtained
Inferential Statistics
methods for drawing and measuring the reliability of
conclusions about a population based on info. obtained from a sample of the population
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Slogerouab # wopue
Observational researchers simply observe characteristics ¿ take We also discuss several other topics like Why are we called homosapien?
measurements
table of random #'s
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Designed Experiment
researchers impose treatments and controls then observe characteristics and take measurements
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Simple Random each possible sample of a given size is equally likely to be
Sampling the one obtained
 w/ replacement member of pop. can be chosen multiple times niess Specified wlo replacement member of pop. can be chosen @most once We also discuss several other topics like What are the basic human needs?
use always
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a sample obtained by simple random
sampling
Simple Random
Sample
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variable
characteristic that varies
(s.no qunu ajoym) pogunos da web
a nonnumerically valued variable If you want to learn more check out What happened to indentured servants who were freed in the early 1600s?
Variable
a measure something
Ja numerically valued variable
P We also discuss several other topics like What is the meaning of catabolism in biochemistry?
Discrete
Continuous
la quantitative vanable whose possible values can be listed
a# of Siblings a quantitative variable whose possible values form some Interval of numbers
(2,5); height; time; weight
never measured equally, variable
some error
qualitative
quantitative
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discrete
continuous
Data
values of a variable
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values of both variables
Qualitative E Quantitahve
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values of both variables
Discrete E Continuous
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Frequency Distribution (qualitative)
la listing of the distint values and their frequencies (in tables
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relative
frequency distribution (qualitative)
a listing of the distinct Values E their relative frequencies
To obtain frequency distribution of data 2. divide each by the total # of observations
M. 53 = 53/99 D.5 = 5/99 5.413 41/99
qualitative
Prep
Pie Chart
la disk divided into wedgeshaped pieces proportional
to the relative frequencies of the qualitative data
a frequency chart  pie chart
13 X 40 310
Bar Chart
distint values of the qualitative data on a horizontal axis and the relative frequencies of those values on a vertical axis
*bars do not touch *
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qual tahve data
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#of Frequ.
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Limit
Grouping
 organizing quantitative data e  use singleValve grouping to make frequency chart
limit grouping tallys
LC cuc
• lower class limit => Smallest value ex) 3039
upper class limit = largest value
• class width diff. between the lower limit of a class and the lower limit of the next higher class
ex) 3039, 40494030=10
• class mark average of the 2 class limits
ex) 3039 30+39/2 69/2 = 34.5
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Cutpoint
Grouping
o lower class wt point → smallest value o upper class wtpoint → smallest value that could go
in the next  higher class
ex:) 120less than 140 + /20  LC
140 less than 160 140 → UC
• class width = difference b/w the wtpoints of a class " class midpoint average of 2 wtpoints of a class
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Histogram
displays the classes of the quantitative data on a horizontal axis and the frequencies of those classes on a vertical axis
*bars Do touch *
Singlevalve → vse distint values of the observations to label the bars, with valve under bar a limit/wtpoint grouping = use LC limits ¿ wtpoints to
label the bars
ex:)
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Dotplots
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130
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Price (6)
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Cotpoint
Grouping
lower class outpoint → smallest value upper class wtpoint a smallest value that could go in the next  higher class
ex) 120ess than 140 120  LC
140 less than 160 140 UC
• class width = difference blw the cutpoints of a class
class midpoint > average of 2 wtpoints of a class
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Histogram
displays the classes of the quantitative data on a horizontal axis and the frequencies of those classes
on a vertical axis
bars Do touch * a singlevalue > use distint values of the observations
to label the bars, with value under bar * limit / wtpoint grouping = use LC limits e cotpoints to
Tabel the bars
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20 30 40 50 60
te LC
DVD Players
Dotplots
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HHHHHHHHHHHHHH TID
120
130
Price (1)
Stem and leaf plot
Stem leaves.
3 468 41296 5 345 6/923 715899
34 36 53 54 69 75 62 63
79 38 41 46
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a
right scewed a more values are
more to the righthand side of the data *left, symmetric
ex.) 149 let
leaf
Stem
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(a) I line per stem
(b) 2 lines per stem
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19
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20 0237889 21 100002345788 20/023
20 7889 04 1st
21 0000234 59 2nd 21. 15788 * Symmetrical, less busy E easier to read
(c) 5 lines per stem
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21 0000
123
21 45 217 21188
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Distribution of a data
set
a table, graph, or formula that provides the values of the observations and how often they occur
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Shapes
(a) bell
(b) triangular (uniform
(d) reverse J
(C) I shaped
(f) right skewed (g) left skewed
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(h) bimodal
Ci multimodal
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several modes in
the data
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measures
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Measures of
Center
mean = sum of observations divided by the # of Observations median= middle valve mode = most reoccming value
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*N total of frequencies
rightskewed
Mo Md
X
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X = Exi Md = (NH) obs
N
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=(22+)  11.5th obs

leftskewed
Y Md Mo
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Symmetric / bell shaped

>
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Sample
mean of observations for a sample
= exe
ne sample size so
*M = Exi
N
population
sample
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Measures
of Variation
•range = maxmin
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Sample Standard Deviation
standard deviation of the observations for a sample
1.) S= {(xix)2 sample mean.
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e sample size more variation in data = larger deviation
Xi  X= deviah on
2.) Exe2 (Exi)/n
& working formula
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ex 1) X: 1,3,5,7,9,11,13
xilxex 1 (xix)
1
6
= 4.32
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310 112
ex 2.)
Exe2= 455
(4x12)/n = 343
455343
4.32
xil xi2 11 3 19 5/25 749
981 111121 13/169
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Three Standard Deviation
X: 1, 3, 5, 7, 9, 11, 13
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Rule
x 35
X +3
S=4.23 S Standard deviation
712.69=  5.69 to
b/w the two
7+12.69=
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19.69
(xS. X+) = 68% of data (825, 8+2) = 95.9% of data (X35, X+ 3) = 99.7% of data
Chebyshev's (XKs, X+ ks)
rat LEAST, could go higher (1Yk2 ) = if K3, then 88.8% of data is shown
(obs)
Rule
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Three Standard Deviation
Rule
X35
X:/ 3,5,7,9,11,13
X=7
S=4.23
S Standard deviation 7+12.69 → 19.69
X +3s
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cant prove
712.69= 6
5,69
b/w the two
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(xS. X+s) = 68% of data. (225, X+25) = 95.9% of data < 2 Std. dew of mean (x35, X+3) = 99.7% of data
Chebyshew's (xKs, X+ ks) 3 Standard deviations
Rule
at LEAST could go higher, but 1*(1%K) jf K = 3, then 88.8% of data is shown Not lower can prove 1 (114) + if k2, then 75% (obs)
Five Number Summary
minimum/st quartile, 2nd, 3rd :maximum
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Md (Q) Q3
Lunaffected by extremes
Md of first 50%
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if there's an even number of data, find the average of the 2 medians for Qa *remember *
arrange the data in increasing or decreasing order Pinterquartile range (IQR) + Q3Q,
? outliers
Lower and Upper Limits
· L Q,  1.5 (IQR) UQz+1.5(IQR)
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Boxplots
find quartiles 12 find the lower and upper limits (adjacent values)
> adjacent values
outliers
5
10
15
20 25 30
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rightskewed
leftskewed
X= {xi : S=
Population (mu)= {xi
sol (pop) N
{(xix2
n1
Mean
(sample) a
o (Sigma) =
(xi/)
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parameter = descriptive measure for population
• Statistic descriptive measure for a sample
(mean), o X (mean), s
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Standardized za  variable Variable
1.score a corresponding value of the standardized variable
(standard score)
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/N Rule
to probability for equally likely outcomes
ft of ways an event can occur Ne total number of possible outcomes
probability
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ex 15.754
77,418
2 03 — 20.3%
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ex) a) the sum of the dice is l
Obles are rolled
 .055 = 5.5% .166 = 16.6%
basic OUP
Properties
probability is always between 0 and / probability of an event that cannot occur is O
event
• probability of an event that must occur is I
certain event
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ex) sum of dice is /
30 + impossible event
Sum of dice is 12 or less
2 = 1 k certain event
Events
sample Space  the collection of all possible outcomes
for an experiment (s) ex: 36 .events a collection of outcomes for the experiment,
that is, any subset of the sample space.
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ex) cards from a deck (52 cards) – sample space
a.) King of hearts b.) King 4/52 { events c.) heart
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(not E)
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Kelationships (hol. E) 201na wentse B
A or B
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o two or more events with no outcomes in common
Mutually Exclusive
Events
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Probability Notation
if Eis an event, then PIE) represents the probability that event occurs
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Special 1. P(A or B) = P(A) + P(B) Addition Rule if they are mutually exclusive
• P(A or B) = P(A) + P(B) P(A and B)
nif they are not mutually exclusive)
general rule.
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• not E
P(E)=1  Plnot E) sp =16.0847.265)
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a.) less than 2000 acres b.) 50 acres or more
event
 fe
et of outcomes
d. spade or face cards
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lex:) Mmale 7.762
E under 18 . 153
P(Mor E) = P(M) + P(E) P(M and E)
= .762 + 153108 .8071
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3 events
. P (A or Borc) = P(A + P (B) + P(C).
= P(A) + P(B) + P(C)  P(A and B)  P (A and C) 
P(B and C) + P (A and B and C)
Thandom uds Variable
. a quantitative variable whose value depends on chance
9 x = vanable * X random variable a discrete a values can be listed
Probability distribution
la listing of the possible values and corresponding
probabilities of a discrete random variable, or a formula I for the probabilities
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Probability histogram
• discrete random Variable = xaxis probability of those values = yaxis
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