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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?

What are the methods for organizing and summarizing information?

Description

School: Texas Tech University
Department: Math
Course: Statistical Methods
Professor: Ram datt joshi
Term: Spring 2017
Tags: Statistics
Cost: 50
Name: MATH 2300 -104
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.
Uploaded: 02/02/2017
17 Pages 29 Views 1 Unlocks
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Study


What are the methods for organizing and summarizing information?



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1-19-17

Descriptive Statistics

methods for organizing and summarizing information

graphs, charts, tables * averages, vanation, percentiles

@ready

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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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

~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 *

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qual tahve data

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#of Frequ.

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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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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

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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 *

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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DVD Players

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Dotplots

110

wdy 120

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) 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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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

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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

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(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

right-skewed

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X

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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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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

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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=

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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

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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

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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) + Q3-Q,

? 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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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)

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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

d. spade or face cards

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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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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