CHAPTER 5CHAPTER 5

Z-ScoresZ-Scores

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Z-ScoresZ-Scores The purpose of The purpose of Z-scoresZ-scores or or Standards Standards

Scores Scores is to identify and describe the is to identify and describe the exact exact locationlocation of every score in a distribution. of every score in a distribution.

Ex. IQ score of 130Ex. IQ score of 130 Characteristics of Z-ScoresCharacteristics of Z-Scores 1. 1. The The meanmean of the Z-scores is equal to of the Z-scores is equal to zerozero.. 2. 2. Every distribution of Z-scores has Every distribution of Z-scores has

standard deviation of 1.standard deviation of 1. 3.3. The The ShapeShape of the distribution of Z-scores is of the distribution of Z-scores is

identical to the shape of the distribution of identical to the shape of the distribution of raw raw scores. scores. 22

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Z-ScoresZ-Scores Transformation of Transformation of X values X values or or

individual scores individual scores into into Z-scores Z-scores serves serves 2 purposes2 purposes

1. 1. It tells the It tells the exact location exact location of the of the score within the distributionscore within the distribution

2. 2. Scores can be Scores can be comparedcompared to other to other distributions that also have been distributions that also have been transformed into Z-scores. transformed into Z-scores.

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Z-ScoresZ-Scores

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XX= = σσ(Z)+(Z)+µµ µµ= X-= X- σσZZ

σσ= (X-= (X-µ)µ)/Z/Z If X=60If X=60

µµ=50=50

σσ=5 Z=?=5 Z=?

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CHAPTER 6CHAPTER 6PProbabilityrobability

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PProbabilityrobability Number of times an event occurs in Number of times an event occurs in

an infinite series of trialsan infinite series of trials

PP= #of times an event = #of times an event occursoccurs//Total number of trials Total number of trials xx100100 P=f/N x 100P=f/N x 100

For probability to be For probability to be accurateaccurate it is it is necessary to use necessary to use random random sampling.sampling.

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CHAPTER 6CHAPTER 6PProbabilityrobability

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PProbabilityrobability Random SamplingRandom Sampling has has 2 requirements:2 requirements: 1. 1. Each individual in the population Each individual in the population

must have an must have an equal chance equal chance of being of being selected.selected.

2. 2. If more than one individual or a If more than one individual or a group of individuals is to be selected group of individuals is to be selected for the sample there must be for the sample there must be ccoonnssttaannt t probability probability for each and every for each and every selectionselection..

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PProbabilityrobability Mega Ball/Power Ball= 1/259mMega Ball/Power Ball= 1/259m Lottery = 1/67mLottery = 1/67m Hit by Lightening = 1/10mHit by Lightening = 1/10m Victim of Crime in theVictim of Crime in the

U.S = 1/8000U.S = 1/8000

Chance of dying in a flight 1/16mChance of dying in a flight 1/16m

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Violent Crime Violent Crime Comparison per Comparison per 1,000 residents 1,000 residents

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Your chances of Your chances of becoming a victim becoming a victim in Florida in Florida 1 in 2051 in 205in Miami is in Miami is 1 in 85 1 in 85

Property Crime Property Crime Rate Rate Comparison per 1,000 residents Comparison per 1,000 residents

2020

Your chances of Your chances of becoming a victim becoming a victim in Florida 1 in 31 in Florida 1 in 31 in Miami 1 in 19 in Miami 1 in 19