Tips for exam 1- Complete all the exercises from the back of each chapter. 2- Make sure you re-do the ones you got wrong! 3- Just before the exam, re-read.

Tips for exam 1- Complete all the exercises from the back of each chapter. 2- Make sure you re-do the ones you got wrong! 3- Just before the exam, re-read all chapters and complete some exercises again! 4- Get used to working with the cheat sheet. 5- Time yourself and work as quickly as possible to acquire fluency. 6- your TA if you have questions! 7- During the exam, be aware of the time. 8- Don’t take too long to solve a problem you don’t know. Leave it for the end. 9- Be neat! (or you run the risk of making unnecessary mistakes!)

Chapter 1: Terms Population: The _______ group of individuals to be studied. Sample: A ________from a __________ Parameter: Describes a ___________ Statistic: Describes a _________ Sampling error: Discrepancy between a _________ and a ____________ ____________statistics: Techniques that summarize and organize a dataset. ___________ statistics: Techniques that use sample data to draw general conclusion about populations.

Chapter 1: Terms Population: The _entire__ group of individuals to be studied. Sample: A _group____from a __population________ Parameter: Describes a _population__________ Statistic: Describes a _sample________ Sampling error: Discrepancy between a _statistic________ and a _parameter___________ __Descriptive__________statistics: Techniques that summarize and organize a dataset. __Inferential_________ statistics: Techniques that use sample data to draw general conclusion about populations.

Chapter 1: Variables Variable: A characteristic or condition that ___________ or has different values for different individuals. ----Height, occupation, temperature, scores in exam, university major, a 5 point rating scale _____, _______, _______ are all discrete variables. _____,_______,________are all continuous variables.

Chapter 1: Variables Variable: A characteristic or condition that __changes_________ or has different values for different individuals. ---Height, occupation, temperature, scores in exam, university major, a 5 point rating scale Occupation, university major, a 5 point- rating scale are all discrete variables. (separate values, no values in between) Height, temperature, exam scores are all continuous variables. (infinite number of possible values)

Chapter 1: Scales of Measurement
Nominal: N_____ Ordinal: O______ Interval and Ratio: Both ordered categories + Both have intervals of same size The difference is the nature of the _______point. Interval: Arbitrary _________ point Ratio: Absolute _______ point (absence of variable) so you can establish ratios! :

Nominal Scale: Name (categories with names, no quantitative distinction) Ordinal Scale: Order (rank observations in terms of size or magnitude) Interval and Ratio Scales: Both ordered categories + Both have intervals of same size The difference is the nature of the _zero______point. Interval Scale: Arbitrary _zero_____point Ratio Scale: Absolute __zero_____ point (absence of variable) so you can establish ratios! :

RoomBSB402; drink sizes (s,m,l); ethnic background; reaction time; temperature; SES (low, mid, high); weight; 0 and 1 for males and females; golf scores (below and above par) Nominal:________________________ Ordinal:_________________________ Interval:_________________________ Ratio: ___________________________ :

Nominal: Room BSB402, 0 and 1 for males and females, ethnic background. Ordinal: Drink sizes (s,m,l), SES (low, mid, high) Interval: temperature, golf scores (below and above par) Ratio: reaction time, weight :

Chapter 1: Measuring two variables
Correlational Method: We _______________ two variables to determine if there is a _____________________________between them. Experimental Method: We _______________one variable and ___________________ the other. We want to determine if there is a _______________________ _____________________between them.

Chapter 1: Measuring two variables
Correlational Method: We ___observe____ two variables to determine if there is a __relationship_______between them. Experimental Method: We ____ manipulate__one variable and ____observe_and measure_ the other. We want to determine if there is a _cause -and -effect relationship _________between them.

Chapter 1: Terms Experimental _______Condition: No treatment
Method _______Condition: Receives treatment _______Variable: Manipulated by researchers. _______Variable: Your scores! The variable that is observed for changes.

Chapter 1: Terms Experimental Control Condition: No treatment
Method Experimental Condition: Receives treatment Independent Variable: Manipulated by researchers. Dependent Variable: Your scores! The variable that is observed for changes.

INDEPENDENT variable Influences CHANGE in the DEPENDENT variable
Chapter 1: Terms INDEPENDENT variable Influences CHANGE in the DEPENDENT variable

Chapter 1: Problems 1- The average salary for a sample of n=20 doctors would be an example of a parameter (TRUE or FALSE?) 2- One characteristic of an experiment is that the researcher manipulates one of the variables being examined (TRUE or FALSE?) 3- A recent study reports that increased lighting during the winter months results in lower depression scores. For this study, what are the IV and DV in this study? 4-After measuring two individuals, a researcher can say that the score of one individual is larger than the score for the other, but it is impossible to say how much larger. What scale of measurement is being used in this situation? (nominal, ordinal, interval, ratio)

Chapter 1: Problems 1- The average salary for a sample of n=20 doctors would be an example of a parameter FALSE. It is a sample! 2- One characteristic of an experiment is that the researcher manipulates one of the variables being examined TRUE 3- A recent study reports that increased lighting during the winter months results in lower depression scores. For this study, what are the IV and DV in this study? Independent V: Levels of lightening Dependent V: Depression scores (depends on lightening!) 4-After measuring two individuals, a researcher can say that the score of one individual is larger than the score for the other, but it is impossible to say how much larger. What scale of measurement is being used in this situation? Ordinal (measures direction but not distance)

Chapter 1: Problems 5- What is the first step to be performed when computing Σ (X-2) 2 ? Square each value Subtract 2 point from each score Sum the values Compute 22 = 4 6- What is the value of Σ (X-1) for the following scores? Scores: 3,4,7

Chapter 1: Problems 5- What is the first step to be performed when computing Σ (X-2) 2 ? Square each value Subtract 2 point from each score Sum the values Compute 22 = 4 6- What is the value of Σ (X-1) for the following scores? Scores: 3,4,7 X X-1 3 2 4 3 7 6 Σ = 11

Chapter 2: Frequency Distribution Table
Use these values to complete the frequency distribution table: 4, 2, 3, 3, 2 , 4, 2, 5, 3, 1 X | f |

Frequency Distribution
Use these values to complete the frequency distribution table: 4, 2, 3, 3, 2 , 4, 2, 5, 3, 1 = 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | 1 | 2 | 3 n = ?? Σ X = ?? M = ??

Frequency Distribution
4, 2, 3, 3, 2 , 4, 2, 5, 3, 1 = 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | 1 | 2 | 3 n = Σ f = 1o Σ X = = 29 M = 29/ 10 = 2.9

Chapter 2 X | f | 1 | 2 | 3 Σ X2 =

Chapter 2 X | f | 1 | 2 | 3 Σ X2 = 52(1) + 42 (2) + 32 (3) + 22 (3) + 12 (1) Σ X2 = 25(1) + 16 (2) + 9 (3) + 4 (3) + 1 (1) OR Σ X2 = Σ X2 = Σ X2 = 97

Chapter 2: Proportions Fraction associated with each score. How many people got a score of 4?p = 2/10 = 0.20 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | p | 1 | | 2 | 0.20 | 3 |

Chapter 2: Proportions Fraction associated with each score. How many people got a score of 4?p = 2/10 = 0.20 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | p | 1 | 0.10 | 2 | 0.20 | 3 | 0.30

Chapter 2: Percentage What percentage of people got a score of 4?
% = x 100 = 20 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | p % | 1 | 0.10 | 2 | % | 3 | 0.30

Chapter 2: Percentage What percentage of people got a score of 4?
% = x 100 = 20 5, 4, 4, 3, 3, 3, 2, 2, 2, 1 X | f | p % | 1 | % | 2 | % | 3 | %

Chapter 2: Practice 3, 2, 3, 2, 4, 1, 2, 4, 5, 2 Create frequency distribution table, find out: n Σ X Σ X2 M To the table, add: Proportions for each score Percentages for each score

Chapter 2: Practice 5, 4, 4, 3, 3, 2, 2, 2, 2, 1 X | f | p %
| 1 | % | 2 | % | 2 | % | 4 | % n= 10 M= 2.8 Σ X = 28 Σ X2 = 92 ( )

Grouped frequency distribution table
Use interval width of 5 points: 82, 75, 88, 93, 53, 84, 87, 58, 72, 94, 69, 84, 61, 91, 64, 87, 84, 70, 76, 89, 75, 80, 73, 78, 60 X | f 90-94 85-89 80-84 75-79 ____ What are the real and apparent limits of 90-94?

94, 93, 91, 89, 88, 87, 87, 84, 84, 84, 82, 80, 78, 76, 75, 75, 73, 72, 70, 69, 64, 61, 60, 58, 53 X f

X f Apparent limit: Real limit: The width of this interval is 5 points (distance between 89.5 to 94.5)

What is the apparent and real limit of a score of x = 40? Apparent limit: Real limit: Lower real limit: Upper real limit: Width of the interval:

What is the apparent and real limit of a score of x = 40? Apparent limit: 40 Real limit: Lower real limit: Upper real limit: Width of the interval: 1 point

X f Guidelines 1- Around 10 intervals 2- Width should be a simple number (2, 5, 10, 20) 3- Bottom score of each interval should be a multiple of width (5 in this case, that is why: 60, 65, 70, etc) 4- All intervals should be the same width

Cumulative frequencies
Construct a grouped frequency distribution table using an interval width of 5 points: 14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11 Guidelines 1- Around 10 intervals 2- Width should be a simple number (2, 5, 10, 20) 3- Bottom score of each interval should be a multiple of width (5 in this case, that is why: 60, 65, 70, etc) 4- All intervals should be the same width

27, 22, 18, 17, 16, 16, 15, 14, 14, 14, 13, 12, 11, 11, 10, 10, 9, 9, 8, 6 X f 5-9 4

Cumulative frequency (cf): How many individuals got a score between or less? X f cf

X f cf How many individuals got a score between or less? How many individuals got a score between or less?

X f cf How many individuals got a score between or less? Cf= 18 How many individuals got a score between or less? Cf= 20

Cumulative percentages
X f cf c% % What percentage of individuals got a score between 5-9 or less? C% = (cf/n) x 100 C% = (4/20) x 100 C% = 20%

X f cf c% % What percentage of individuals got a score between or less? C% = (cf/n) x 100 C% =

X f cf c% % % What percentage of individuals got a score between or less? C% = (cf/n) x 100 C% = (13/20) x 100 C% = 65%

X f cf c% % % % % % A score of x= 11 has a percentile rank of 65% A score of x=11 is the 65th percentile

X f cf c% % % % % % A score of x= 22 has a percentile rank of ____ A score of x= 22 is the ___ percentile

X f cf c% % % % % % A score of x= 22 has a percentile rank of 95% A score of x= 22 is the 95th percentile

Interpolation X f cf c% 25-29 1 20 100% 20-24 1 19 95% 15-19 5 18 90%
% % % % % What is the 95th percentile? 24.5 (upper limit of percentile rank). We know that all the numbers in that rank are below the upper limit of 24.5 What is the 90th percentile? What is the 20th percentile?

% % % % % What is the 90th percentile? 19.5 What is the 20th percentile? 9.5

% % % % % What is the percentile rank for 24.5? 95%

Interpolation Find the 50th percentile X f cf c% 25-29 1 20 100%
% % % % %

Interpolation Find the 50th percentile X c% 25-29 100% 20-24 95%
% % % % %

Interpolation Find the 50th percentile X c% 10-14 65%
% ____ 50% points points % Width of c% = 45 points Distance between 50% and upper limit = 15 points 15/45 = 1/3 So 50% is 1/3 below the upper limit 50% is 1/3 below 65%

Interpolation So the 50th percentile must be 1/3 below the upper limit of a rank that has a width of 5 points (9.5 to 14.5) X c% % (1/3 below 14.5) 50% (1/3 below 65%) %

Interpolation 1/3 x 5 = 1.67 Width of X is 5 points. What is 1/3 of 5?
X c% % 1/3 below % % 1/3 x 5 = 1.67

Interpolation So the 50th percentile is below the upper limit of a rank that has a width of 5 points (9.5 to 14.5) X c% % 1/3 below % % 14.5 – 1.67 = 12.83

Interpolation X c% % % %

Interpolation Find the 50th percentile X c% 20-24 100% 15-19 90%
% % % % %

Interpolation Find the 50th percentile X c% 5-9 60% _____ 50% 0-4 10%
% _____ % % Width Width ___ points (4.5 to 9.5) ___________ Distance with upper limit ___________ Fraction distance ___________

Interpolation Find the 50th percentile X c% 5-9 60% _____ 50% 0-4 10%
% _____ % % Width Width 5 points (4.5 to 9.5) 50 points (60-10) Distance with upper limit points ( ) Fraction distance 1/5 (10/50, 10 out of 50) 50% is 1/5 below upper limit

Interpolation Find the 50th percentile X c% 9.5 60% _____ 50% 4.5 10%
% _____ % % Width Width 5 points (4.5 to 9.5) 50 points (60-10) Fraction distance Fraction distance with with upper limit upper limit __/__ below ____ /5 below 60%

% _____ % % Width Width 5 points (4.5 to 9.5) 50 points (60-10) Fraction distance Fraction distance with with upper limit upper limit 1/5 below /5 below 60% What is 1/5 of 5? _______

% _____ % % Width Width 5 points (4.5 to 9.5) 50 points (60-10) Fraction distance Fraction distance with with upper limit upper limit 1/5 below /5 below 60% What is 1/5 of 5? 1

% _____ % % So the value is 1 point below 9.5 _____________= _______

% _____ % % So the value is 1 point below 9.5 ___ __________= __8.5_____

Interpolation Find the the percentile rank for x= 12 X c% 14-15 100%
% % % % % % %

Find the the percentile rank for 13 X c% 12-13 94% 10-11 82%
Interpolation Find the the percentile rank for 13 X c% % %

Interpolation Find the the percentile rank for 12 X c% 13.5 94% 12
% 12 % Width Width _____ points _____points Distance from upper limit _____points Fraction of total _________

Interpolation Find the the percentile rank for 12 X c% 13.5 94% 12
% 12 % Width Width 2 points points Distance from upper limit 1.5 points Fraction of total 1.5/2 = 0.75 (3/4)

Interpolation Find the the percentile rank for 12 X c% 13.5 94%
% ____ % What is ¾ below 94%? (3/4 of 94) __________= ____

Interpolation Find the the percentile rank for 12 X c% 13.5 94%
% ____ % What is ¾ below 94%? ¾ x 12 (width) = 9

Interpolation Find the the percentile rank for 12 X c% 13.5 94% 12 85%
% % % 94 – 9 = 85

% % % % % % %

% _______ % Width: 2 points (3.5 to 5.5) Width: 8

Interpolation Find the the percentile rank for x= 5 X c% 5.5 10%
% _______ % Width: 2 points Width: 8 Distance from top: 0.5 0.5/2 = 0.25 (1/4)

Interpolation Find the the percentile rank for x= 5 X c% 5.5 10% 5 8%
% % % Width: 8 ¼ x 8 = 2 10 – 2 = 8%

Chapter 3 _____________ ________________ determines which single score defines the centre of the distribution. It looks for the single score that is the most typical and most representative of the entire group.

Central Tendency Central Tendency determines which single score defines the centre of the distribution. It looks for the single score that is the most typical and most representative of the entire group. Which 3 methods are used to measure central tendency? 1- 2- 3-

Central Tendency Which 3 methods are used to measure central tendency?
1- Mean 2- Median 3- Mode

Central Tendency Σ X/n is the __________
The midpoint of the list is the ___________ The score or category that has the greatest frequency is the _______________

Central Tendency Σ X/n is the mean
The midpoint of the list is the median The score or category that has the greatest frequency is the mode

Central Tendency Compute the mean, median and mode for the scores shown in the frequency distribution table: X f 7 1 6 1 5 1 4 1 3 4 2 3 1 1

Central Tendency Compute the mean, median and mode for the scores shown in the frequency distribution table: X f Mean: 3.42 7 1 6 1 Mode: 3 5 1 4 1 Median: 3 ,2,2,2,3,3||3,3,4,5,6,7 2 3 1 1

Central Tendency What is the median? 3, 5, 8, 10, 11 1, 1, 4, 5, 7, 8

Central Tendency What is the median? 3, 5, 8, 10, 11 8
1, 1, 4, 5, 7, 8 4.5

Central Tendency What is the median? 1, 2, 3, 4, 4, 4, 4, 5, 6, 7

Central Tendency What is the median? 1, 2, 3, 4, 4 ||| 4, 4, 5, 6, 7 4

Central Tendency What is the median? 1, 2, 3, 4 ||| 4, 4, 4, 6
What is the real limit of 4? 3.5 to 4.5 What is the width of this interval? 1 point How many parts in the interval of 4? 4 parts What is the lower limit of 4? 3.5 How many parts of 4 are included before the median line? One (there are three after the line) 3.5 + ¼ = 3.75

Central Tendency What is the median? 1, 2, 2, 3, 4 , 4, 4, 4, 4, 5
What is the real limit of 4? ______ What is the width of this interval? _______ In how many parts in the interval of 4? _______ What is the lower limit of 4? _______ How many parts of 4 are included before the median line? _______ ___________

Central Tendency What is the median? 1, 2, 2, 3, 4 ||| 4, 4, 4, 4, 5
What is the real limit of 4? 3.5 to 4.5 What is the width of this interval? 1 point In how many parts in the interval of 4? 5 parts What is the lower limit of 4? 3.5 How many parts of 4 are included before the median line? One (there are four after the line) /5 = 3.70

Central Tendency What is the median? 1, 2,3 ||| 3, 3, 4
What is the real limit of 3? What is the width of this interval? In how many parts in the interval of 4? What is the lower limit of 4? How many parts of 4 are included before the median line?

Central Tendency What is the median? 1, 2,3 ||| 3, 3, 4
What is the real limit of 3? 2.5 to 3.5 What is the width of this interval? 1 point In how many parts in the interval of 4? 3 parts What is the lower limit of 4? 2.5 How many parts of 4 are included before the median line? One (there are two after the line) /3 = 2.83

Chapter 4 Dr. Mode and Dr. Mean offer stats tutorial classes. These are the scores their students got in the final exam: Dr. Mode Dr. Mean M = M =

Chapter 4 Dr. Mode Dr. Mean 7 10 8 10 7 4 7 9 8 3 6 10 6 3 M = 7 M = 7
M = M = 7 1- Which one do you think will have the biggest variability? 2- Who would you choose and why?

Chapter 4 Variability: Are the scores clustered together or spread out over a large distance? Three measures of variability: Range: Distance covered by scores in distribution Variance: Average squared distance from mean Standard Deviation: Average distance from the mean. (square root of variance)

Chapter 4 Variability: Are the scores clustered together or spread out over a large distance? If we want to find out the variance in Dr. Mode’s students, what should we do first?

X (Dr. Mode) Deviation from mean 7 0 (7 -7) 8 1 (8-7) 7 8 6 M = 7
Variability X (Dr. Mode) Deviation from mean (7 -7) (8-7) 7 8 6 M = 7

Variability X Deviation from mean 7 0 (7 -7) 8 1 (8-7) 7 0 (7-7)
(7 -7) (8-7) (7-7) (6-7) M = 7 What is the mean of the deviations?

Variability X Deviation from mean 7 0 (7 -7) 8 1 (8-7) 7 0 (7-7)
(7 -7) (8-7) (7-7) (6-7) M = 7 What is the mean of the deviations? = 0 This is because the total of the distances above the mean is the same as the total of the distances below the mean.

X Deviations Squared deviations 7 0 0 8 1 1 7 0 8 1 6 -1
Variability X Deviations Squared deviations 7 0 8 1 6 -1

Variability 7 0 0 8 1 1 6 -1 1 6 -1 1 X Deviations Squared deviations
What is the sum of the squared deviations? SS =

Variability X Deviations Squared deviations 7 0 0 8 1 1 6 -1 1 6 -1 1
What is the sum of the squared deviations? SS = 4 What is the mean of the squared deviations? σ 2= SS/N σ 2= ____________

Variability X Deviations Squared deviations 7 0 0 8 1 1 6 -1 1 6 -1 1
What is the sum of the squared deviations? SS = 4 What is the mean of the squared deviations? σ 2= SS/N σ 2= This is the VARIANCE  **But variance is a squared distance and the concept is hard to interpret

Variability σ 2= 0.5714--------variance
X Deviations Squared deviations σ 2= variance What is the standard deviation? √SS/N or √σ 2 σ =

Variability σ 2= 0.5714--------variance
X Deviations Squared deviations σ 2= variance What is the standard deviation? √SS/N or √σ 2 σ = (average distance from mean)

SS X (X-μ) (X-μ)2 What is the sum of the squared deviations? Definitional formula SS = Σ (x-μ ) 2 SS = 4 Computational formula SS = ΣX2 – (ΣX)2 _______ N

Computational formula
X ΣX2 7 49 8 64 6 36 ΣX= 49 ΣX2 = 347 SS = ΣX2 – (ΣX)2 _______ N SS = 347 – (49)2 7 SS = 347 – SS = 4

Calculate mean, SS, variance and standard deviation Dr. Mean 10 4 9 3
Chapter 4 Calculate mean, SS, variance and standard deviation Dr. Mean 10 4 9 3

Chapter 4 Dr. Mean X2 10 100 4 16 9 81 3 9 ΣX= 49 ΣX2 = 415
4 16 9 81 3 9 ΣX= 49 ΣX2 = 415 μ= ΣX/N (49/7) μ = 7 (Population mean) SS = ΣX2 – (ΣX)2 _______ N SS = 415 – (49)2/ SS = 415 – SS = 72 (sum of sq. devia.) σ 2= SS/N / σ 2 = (variance) σ = √σ 2 = √ σ = (standard deviation)

Chapter 4 Dr. Mode Dr. Mean 7 10 8 10 7 4 7 9 8 3 6 10 6 3 M = 7 M = 7
M = M = 7 1- Which one do you think will have the biggest variability? Dr. Mode Dr. Mean σ 2= (variance) σ 2= (variance) σ = (sd) σ = (sd)

Mean Sum of Squared Deviations Variance Standard Deviation Population μ= ΣX/N) SS = Σ (X-μ ) 2 or: SS = ΣX2 – (ΣX)2 _______ N σ 2= SS/N σ = √SS/N Sample M= ΣX/n) SS = Σ (X-M ) 2 0r: n s 2= SS/n-1 s 2= SS/df s = √SS/n-1 s = √SS/df

Chapter 4: Practice Calculate SS, variance and sd for the following scores (both for a population and a sample): X 5 3 2 4 1

Population SS = 10 σ 2= 2 σ = 1.4142 Sample s2 = 2.5 s= 1.5811
Chapter 4: Practice Population SS = 10 σ 2= 2 σ = Sample s2 = 2.5 s=

Chapter 5

Z-scores Example a (μ= 70 // σ = 3) 73= +1 76 = +2 67 = -1 64 = -2
Example b (μ= 70 // σ = 12) 82 = +1 88 = +1.5 58= - 1 52= - 1.5

Z-scores z = X – μ σ Example a (μ= 70 // σ = 3)
What is the z-score of 73? z= 73 – 70 3 z= + 1 Use the formula to find z-scores for 76 and 64

Z-scores z = X – μ σ Example a (μ= 70 // σ = 3)
What is the z-score of 76? z= 76 – 70 3 z= + 2 What is the z-score of 64? z= 64 – 70 z= - 2

Z-scores z = X – μ σ Example b (μ= 70 // σ = 12)
What is the z-score of 88? What is the z-score of 58?

What is the z-score of 88? z= 88 – 70 12 z= + 1.5 What is the z-score of 58? z= 58 – 70 z= - 1

Z-scores A z-score tells you the precise location of each X value within a distribution. z= >means 1 standard deviation above the mean z= >means 3 standard deviations below the mean

Chapter 5

What score corresponds to a z-score of + 1.5? + 1.5= X – (1.5 x 3) X = 74.5 3 What score corresponds to a z-score of + 0.5? What score corresponds to a z-score of - 2.5?

Z-scores - 2.5= X – 70------- (-2.5 x 3) + 70------X = 62.5 z = X – μ
σ Example b (μ= 70 // σ = 3) What score corresponds to a z-score of + 1.5? + 1.5= X – (1.5 x 3) X = 74.5 3 What score corresponds to a z-score of + 0.5? + 0.5= X – (0.5 x 3) X = 71.5 What score corresponds to a z-score of - 2.5? - 2.5= X – (-2.5 x 3) X = 62.5

Z-scores: Practice 1- For a population with μ = 80 and σ = 12, what is the z-sc0re corresponding to x = 74? 2- For a population with μ= 100 and σ=20, what x value corresponds to z = + 1.5? 3- For a population with a mean of μ =70, a score that is located 10 points below the mean would have a z-score of..? 4- In a population with μ =60, a score of x = 58 corresponds to a z- score of z=-.50. What is the population sd? 5- You have a score of X=65 on an exam. Which set of parameters would give you the best grade on the exam? (a) μ = 60 and σ = 10 (b) μ = 60 and σ = 5 (c ) μ = 70 and σ = 10 (d) μ = 70 and σ = 5

Z-scores: Practice 1- (74-80)/12 ------ z = - 0.50
2- (1.5 x 20) z = 130 3- We don’t know, we don’t have the sd 4- σ= (58-60)/ σ = 4 5- You have a score of X=65 on an exam. Which set of parameters would give you the best grade on the exam? (a) μ = 60 and σ = 10 (b) μ = 60 and σ = 5 (c ) μ = 70 and σ = 10 (d) μ = 70 and σ = 5

Standardize Distributions
X 6 5 2 3 N = μ = σ =

X 6 5 2 3 N = 6 μ = ΣX/N μ = 18/ μ = 3 SS = ΣX2 – (ΣX)2 _______ N SS = 78 – (18)2/6 SS = 78 – SS = 24 σ = √SS/N σ = √24/ σ =√ σ = 2

X 6 5 2 3 Draw a histogram of the distribution Convert each X value to a z-score.

X 0 z= (0-3)/ 6 5 2 3 z = X – μ σ

X 0 z= (0-3)/2 z= -1.50 6 z= (6-3)/2 z= +1.50 5 z= (5-3)/2 z= 2 z= (2-3)/2 z= -0.50 3 z= (3-3)/2 z= 0 z = X – μ σ Draw a histogram with using the z-scores.

Standardize a distribution t0 create a new one
What are the z-scores for 29, 43, 57, 71 and 85?

Creating a new distribution
X 29 z= (29-57)/14 z= -2 43 57 71 85 μ= 57 σ = 14 z = X – μ σ

X 29 z= (29-57)/14 z= -2 43 z= (43-57)/14 z= -1 57 z= (57-57)/14 z= 0 71 z= (71-57)/14 z= +1 85 z= (85-57)/14 z= 2 μ= 57 σ = 14 z = X – μ σ

Create a new distribution with μ = 50 and σ= 10. How?

Convert the z-scores into an X value using μ = 50 and σ= 10

Original X Z –scores New X 29 z= -2 (-2x10) 43 z= -1 57 z= 0 71 z= +1 85 z= 2 new μ= 50 new σ = 10 z = X – μ σ

Original X Z –scores New X 29 z= -2 (-2x10) 43 z= -1 (-1x10) 57 z= 0 (0 x10) 71 z= +1 (1 x10) 85 z= 2 (2 x10) new μ= 50 new σ = 10 z = X – μ σ

Tips for exam 1- Complete all the exercises from the back of each chapter. 2- Make sure you re-do the ones you got wrong! 3- Just before the exam, re-read.

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Tips for exam 1- Complete all the exercises from the back of each chapter. 2- Make sure you re-do the ones you got wrong! 3- Just before the exam, re-read.

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Presentation on theme: "Tips for exam 1- Complete all the exercises from the back of each chapter. 2- Make sure you re-do the ones you got wrong! 3- Just before the exam, re-read."— Presentation transcript:

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