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TTU / Math / MATH 2300 / What are the methods for organizing and summarizing information?

# What are the methods for organizing and summarizing information? Description

##### Description: Here is the "study guide" for the test coming up. I don't ever make study guides myself for the tests, I just look at my notes, but these are all the notes up until this week and I will post the last set that I take this week early next week. For Statistical methods with Professor Joshi.
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## What are the methods for organizing and summarizing information?

U sud ou

1-19-17

Descriptive Statistics

methods for organizing and summarizing information

graphs, charts, tables * averages, vanation, percentiles

happened

"descnbe" the data

## What is the collection of all individuals or items under consideration in a statistical study?

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

STOV SOL

## What is the part of the population from which information is obtained?

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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aple

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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les

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1-24-17

KudySON

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

~M- 53

of some sore) D-5 S-41

of

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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 wedge-shaped 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 *

sapunboy

China Brazil

qual tahve data

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#of Frequ.

Srdy Soup

011

Limit

Grouping

- organizing quantitative data e - use single-Valve grouping to make frequency chart

limit grouping tallys

LC cuc

• lower class limit => Smallest value ex) 30-39

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) 30-39, 40-4940-30=10

• class mark average of the 2 class limits

ex) 30-39 30+39/2 69/2 = 34.5

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dys

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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:) 120-less 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

Stud Soup

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 *

Single-valve → 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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20 30 40 50 60

te LC

DVD Players

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Dotplots

110

wdy 120

130

0

Price (6)

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dy

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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) 120-ess 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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Soup

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 single-value > 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

Stud sou

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20 30 40 50 60

te LC

DVD Players

Dotplots

| Studs soup

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 right-hand 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 0-4 1st

21 0000234 5-9 2nd 21. 15788 * Symmetrical, less busy E easier to read

(c) 5 lines per stem

| Study Soup

21 0000

123

21 45 217 21188

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

1-31-17

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

right-skewed

Mo Md

X

TSV SOU

702 808

Mo-80 the

X = Exi Md = (NH) obs

N

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=(22+) - 11.5th obs

-

left-skewed

Y Md Mo

dy Sous

Symmetric / bell shaped

-----

>

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Judy Soup

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 = max-min

U study

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Sample Standard Deviation

standard deviation of the observations for a sample

1.) S= {(xi-x)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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R-1

ex 1) X: 1,3,5,7,9,11,13

xilxe-x 1 (xi-x)

1

-6

= 4.32

J7-1

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310 112

ex 2.)

Exe2= 455

(4x12)/n = 343

455-343

4.32

xil xi2 11 3 19 5/25 749

981 111121 13/169

Sody Soup

Study

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Three Standard Deviation

X: 1, 3, 5, 7, 9, 11, 13

V SOL

Rule

x 35

X +3

S=4.23 S- Standard deviation

7-12.69= - 5.69 to

b/w the two

7+12.69=

Study Soup

19.69

(x-S. X+) = 68% of data (8-25, 8+2) = 95.9% of data (X-35, X+ 3) = 99.7% of data

Chebyshev's (X-Ks, X+ ks)

rat LEAST, could go higher (1-Yk2 ) = if K-3, then 88.8% of data is shown

(obs)

Rule

Studs Sou

Sou

Study S

@study

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Three Standard Deviation

Rule

X-35

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

7-12.69= 6

-5,69

b/w the two

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(x-S. X+s) = 68% of data. (2-25, X+25) = 95.9% of data < 2 Std. dew of mean (x-35, X+3) = 99.7% of data

Chebyshew's (x-Ks, 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 (1-14) + if k-2, then 75% (obs)

Five- Number Summary

minimum-/st quartile, 2nd, 3rd :maximum

Sudy So

Md (Q) Q3

Lunaffected by extremes

Md of first 50%

Study Soup

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) + Q3-Q,

? outliers

Lower and Upper Limits

· L Q, - 1.5 (IQR) UQz+1.5(IQR)

Study SP

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Boxplots

find quartiles 12 find the lower and upper limits (adjacent values)

outliers

5

10

15

20 25 30

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right-skewed

left-skewed

X= {xi : S=

Population (mu)= {xi

sol (pop) N

{(xi-x2

n-1

Mean

(sample) a

o (Sigma) =

(xi-/)

udson

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 /

3-0 + 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)

AEB

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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

coup

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.

dysc

• not E

-P(E)=1 - Plnot E) sp =1-6.0847.265)

-10.6511

a.) less than 2000 acres b.) 50 acres or more

event

- fe

et of outcomes

22:42

lex:) M-male 7.762

E under 18 . 153

P(Mor E) = P(M) + P(E)- P(M and E)

= .762 + 153-108 -.8071

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Stud SON

Studys

Sud Sour

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

o stua

Probability histogram

• discrete random Variable = x-axis probability of those values = y-axis

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