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# BASIC NOTATION - PowerPoint PPT Presentation

BASIC NOTATION. X i = The number of meals I have on day “ i ” X= 1,2,3,2,1  X i = ???  X i 2 = ??? ( X i ) 2 = ???. Summation (). 9. 19. 81. Nominal Political affiliation Republican Democrat Independent Gender Female Male. Qualitative Variables.

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Xi = The number of meals I have on day “i”

X= 1,2,3,2,1

 Xi = ???

 Xi2 = ???

( Xi)2 = ???

Summation ()

9

19

81

Political affiliation

Republican

Democrat

Independent

Gender

Female

Male

Qualitative Variables

Categories have relative value/order

Example

Very Depressed

Depressed

Slightly depressed

Not depressed

Quantitative Variables

Categories have relative value/order

Difference in measurement = Difference in characteristic

Example

Temperature Fahrenheit, 83,84,85 …

Difference from 83 to 84 = Difference from 84 to 85

Quantitative Variables

Categories have relative value/order

Difference in measurement = Difference in characteristic

True zero (0) point exists

Example

Temperature Kelvin, 0,1,2,…343,345,346 …

Height 0 inches, 1 inch, …. 86 inches (Shaq)

Quantitative Variables

Ungrouped (list of scores)

Grouped (grouped by ranges)

Graphs

histograms

frequency polygons

Frequency Distributions

The variable: Time (in minutes) between getting out of bed this morning and eating your first bite of food.

Time (min) Ungrouped :

(6, 28, 27, 7, 7, 24, 39, 55, 13, 17, 13, 13, 3, 23, 18, 37, 2, 8, 11, 18, 22, 2, 21, 31, 12)

Table Distributions

Bad Grouped Frequency DistributionXf 0-10 7 11-20 8 21-30 6 31-40 3 41-50 0 51-60 1 25

Good Grouped Frequency DistributionXf1-10 7 11-20 8 21-30 6 31-40 3 41-50 0 51-60 1 25

Modality - Peaks this morning and eating your first bite of food.

Symmetry – Mirror Reflection

Asymptoticness – Extreme Values on both Sides

Distribution Characteristics

USA this morning and eating your first bite of food.

Unimodal

Symmetric

Asymptotic

Normal Distributions

Inflection points this morning and eating your first bite of food.

Where curve changes from

convex to concave or

concave to convex

Also = 1 standard deviation from the mean

CENTRAL TENDENCY this morning and eating your first bite of food.WHAT IS A TYPICAL SCORE LIKE?

Mode: Most common value; number of peaks; always an observed value

Median: Middle of distribution; not affected much by outliers

Mean: Average; greatly affected by outliers

CENTRAL TENDENCY this morning and eating your first bite of food.Modes

• Most common score(s)

1,2,2,2,3,4,5,6,7 Unimodal Mode=2

1,3,3,4,4,5,6,7,8 Bimodal Modes=3,4

1,3,3,4,4,5,6,6,8 Trimodal Modes=3,4,6

1,2,3,4,5,6,7,8,9 Amodal

Modes in Populations this morning and eating your first bite of food.

• Unimodal

• Bimodal

• Trimodal

• Amodal ?

CENTRAL TENDENCY this morning and eating your first bite of food.Medians

• Middle score in distribution

• Odd number of scores

5-point data set: 2,3,5,9,12 Median=5

1,2,5,5,7,9,500,700,999 Median=?

• Even number of scores

4-point data set: 3,5,8,9 Median=(5+8)/2=6.5

1,2,5,5,7,9,500,700,999,1122

Median=?

Medians in Populations this morning and eating your first bite of food.

CENTRAL TENDENCY this morning and eating your first bite of food.Means

More modes, medians and means this morning and eating your first bite of food.

How different are scores from central tendency? this morning and eating your first bite of food.

Range

Standard Deviation

Highest value – Lowest Value this morning and eating your first bite of food.

Affected only by end points

Data set 1

1,1,1,50,99,99,99

Data set 2

1,50,50,50,50,50,99

Why ‘range’ is weak this morning and eating your first bite of food.

How different are scores from central tendency? this morning and eating your first bite of food.

Always, by definition of the mean

Population this morning and eating your first bite of food.Standard Deviation

Sample Variance and this morning and eating your first bite of food.Standard deviation

Also known as

“Estimated Population Standard Deviation”

Sample Variance and this morning and eating your first bite of food.Standard deviation

Why do we use N-1 for sample?

Because sample means are closer to sample

mean than to population mean, which underestimates the estimate

Population 2,4,6,and 8, σ = (2+4+6+8)/4 = 5

Scores 2 and 6

σ2= (2-5)2 +(6-5)2 = 9 + 1 = 10

Scores 2 and 6, = (2+6)/2 = 4

S2= (2-4)2 +(6-4)2 = 4 + 4 = 8

Sample Variance this morning and eating your first bite of food.

 SUM OF SQUARED DEVIATIONS

 DEGREES OF FREEDOM

STANDARD DEVIATION

Differences Between this morning and eating your first bite of food.Sample and Population Standard Deviation

1) Sigma vs. S

2) Population mean versus Sample mean

3) N vs. N-1

Super Important Relationship this morning and eating your first bite of food.Standard Deviation is square root of variance

SAMPLE STANDARD DEVIATION =

SQUARE ROOT OF THE SAMPLE VARIANCE

POPULATION STANDARD DEVIATION =

SQUARE ROOT OF THE POPULATION VARIANCE

Population Standard Deviation this morning and eating your first bite of food.

Sample Standard Deviation this morning and eating your first bite of food.