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Презентация на тему Measures of variation. Week 4 (1)

Numerical measures to describe data COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALLCh. 2-MeanMedianMode Describing Data NumericallyVarianceStandard DeviationCoefficient of VariationRangeInterquartile RangeCentral TendencyVariationQuartile
BBA182 Applied Statistics Week 4 (1)Measures of variationDR SUSANNE HANSEN SARALEMAIL: SUSANNE.SARAL@OKAN.EDU.TRHTTPS://PIAZZA.COM/CLASS/IXRJ5MMOX1U2T8?CID=4#WWW.KHANACADEMY.ORGDR SUSANNE HANSEN SARAL Numerical measures to describe data Interquatile range, IQR 		Alternative way to calculate the IQR Five-Number Summary of a data setDR SUSANNE HANSEN SARALIn describing numerical data, Five-Number Summary: Example         	DR Five number summary and BoxplotsBoxplot is created from the five-number summaryA boxplot Five number summary and BoxplotsBoxplot is created from the five-number summaryThe central Five number summary and boxplot  Five number summary and boxplot  Boxplot COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING Gilotti’s Pizza Sales in $100s Gilotti’s Pizza Sales  What are the shapes of the distribution Gilotti’s Pizza Sales - boxplot Gilotti’s Pizza Sales in $100s Measuring variation in a data set     that follows Measuring variation in a data setData set 1 : 23  19 Average distance to the mean: Calculating the average distance to the mean 2/22/2017 Calculating the average distance to the mean 2/22/2017 Calculating the average distance to the meanNotice that the deviation score Calculating the average distance to the mean Step 3: The solution  Average of squared deviations from the meanPopulation variance:COPYRIGHT © 2013 PEARSON EDUCATION,  Average of squared deviations from the meanSample variance:COPYRIGHT © 2013 PEARSON EDUCATION,  Most commonly used measure of variation in a population Shows variation about Sample Standard Deviation, sMost commonly used measure of Calculation Example: 	Sample Standard Deviation, sCOPYRIGHT © 2013 PEARSON EDUCATION, Class example Calculating sample variance and standard deviation DR SUSANNE HANSEN SARAL Class example (continued) DR SUSANNE HANSEN SARAL Class example (continued)The mean = 7 DR SUSANNE HANSEN SARAL 6 C		      Class example (continued) DR SUSANNE HANSEN SARAL
Слайды презентации

Слайд 2 Numerical measures to describe

Numerical measures to describe data

data


COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-

Mean

Median

Mode

Describing Data Numerically

Variance

Standard Deviation

Coefficient of Variation

Range

Interquartile Range

Central Tendency

Variation

Quartile


Слайд 3 Interquatile range, IQR


Alternative way to calculate the

Interquatile range, IQR 		Alternative way to calculate the IQR

IQR

Khan Academy

Слайд 5
Five-Number Summary of a data set
DR SUSANNE HANSEN

Five-Number Summary of a data setDR SUSANNE HANSEN SARALIn describing numerical

SARAL
In describing numerical data, statisticians often refer to the

five-number summary. It refers to five the descriptive measures we have looked at:
minimum value
first quartile
median
third quartile
maximum value

minimum < Q1 < median < Q3 < maximum

It gives us a good idea where the data is located and how it is spread in the data set


Слайд 6 Five-Number Summary: Example

Five-Number Summary: Example     	DR SUSANNE HANSEN SARAL


DR SUSANNE HANSEN SARAL


minimum < Q1 < median < Q3 < maximum

6 < 7.75 < 10.5 < 12.25 < 14

Sample Ranked Data: 6 7 8 9 10 11 11 12 13 14



Слайд 7

ExerciseConsider the data given below:

Exercise
Consider the data given below:

 110 125 99 115 119 95 110 132 85

a. Compute the mean.
b. Compute the median.
c. What is the mode?
d. What is the shape of the distribution?
e. What is the lower quartile, Q1?
f. What is the upper quartile, Q3?
g. Indicate the five number summary
 


Слайд 8

ExerciseConsider the data given below. 85

Exercise
Consider the data given below.
 85

95 99 110 110 115 119 125 132
a. Compute the mean. 110
b. Compute the median. 110
c. What is the mode? 110
d. What is the shape of the distribution? Symmetric, because mean = median=mode
e. What is the lower quartile, Q1? 97
f. What is the upper quartile, Q3? 122
g. Indicate the five number summary 85 < 97 < 110 < 122 < 132

 


Слайд 9 Five number summary and Boxplots

Boxplot is created from

Five number summary and BoxplotsBoxplot is created from the five-number summaryA

the five-number summary

A boxplot is a graph for numerical

data that describes the shape of a distribution, in terms of the 5 number summary.

It visualizes the spread of the data in the data set.


COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-


Слайд 10 Five number summary and Boxplots
Boxplot is created from

Five number summary and BoxplotsBoxplot is created from the five-number summaryThe

the five-number summary

The central box shows the middle half

of the data from Q1 to Q3, (middle 50% of the data) with a line drawn at the median

Two lines extend from the box. One line is the line from Q1 to the minimum value, the other is the line from Q3 to the maximum value

A boxplot is a graph for numerical data that describes the shape of a distribution, like the histogram


COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-


Слайд 11

Five number summary and boxplot 

Five number summary and boxplot
 


Слайд 12 Five number summary and boxplot
 

Five number summary and boxplot 

Слайд 13 Boxplot
COPYRIGHT © 2013 PEARSON

Boxplot COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS

EDUCATION, INC. PUBLISHING AS PRENTICE HALL
Ch. 2-

Median
(Q2)

maximum


minimum

Q1
Q3
Example:
25%

25% 25% 25%

12 30 45 57 70

The plot can be oriented horizontally or vertically






Слайд 14 Gilotti’s Pizza

Gilotti’s Pizza Sales in $100s

Sales in $100s


Слайд 15 Gilotti’s Pizza Sales What are the shapes

Gilotti’s Pizza Sales What are the shapes of the distribution of the four data set?

of the distribution of the four data set?


Слайд 16 Gilotti’s Pizza

Gilotti’s Pizza Sales - boxplot

Sales - boxplot


Слайд 17 Gilotti’s Pizza

Gilotti’s Pizza Sales in $100s

Sales in $100s


Слайд 18 Measuring variation in a data set

Measuring variation in a data set   that follows a

that follows a normal distribution
COPYRIGHT © 2013 PEARSON

EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-

Small spread/variation

Large spread/variation


Слайд 19 Measuring variation in a data set


Data set 1

Measuring variation in a data setData set 1 : 23 19

: 23 19 21 18

24 21 23 Mean: 21.3

Data set 2 : 23 35 19 7 21 24 22 Mean: 21.6

Which of these two data sets has the highest spread/variation? Why?

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-


Слайд 20 Average distance to the

Average distance to the mean: 		  Standard deviationMost

mean: Standard deviation


Most commonly used measure of

variability

Measures the standard (average) distance of each individual data point from the mean.

2/22/2017


Слайд 21 Calculating the average distance to the mean
 
2/22/2017

Calculating the average distance to the mean 2/22/2017

Слайд 22 Calculating the average distance to the mean
 
2/22/2017

Calculating the average distance to the mean 2/22/2017

Слайд 23 Calculating the average distance to the mean


Notice

Calculating the average distance to the meanNotice that the deviation

that the deviation score adds up to zero!

This is

not surprising because the mean serves as balance point (middle point) for the distribution. (!Remember: In a symmetric distribution the mean and the median are identical)
The distances of the single score above the mean equal the distances of the single scores below the mean.
Therefore the deviation score always adds up to zero.

2/22/2017


Слайд 24 Calculating the average distance to the mean

Calculating the average distance to the mean Step 3: The



Step 3: The solution is to get rid of

the + and – which causes the cancelling out effect. We square each deviation score and sum them up

2/22/2017


Слайд 25  
Average of squared deviations from the mean

Population variance:
COPYRIGHT

 Average of squared deviations from the meanPopulation variance:COPYRIGHT © 2013 PEARSON

© 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL
Ch.

2-

Where:

= population mean
N = population size
xi = ith value of the variable x


Слайд 26  
Average of squared deviations from the mean

Sample variance:
COPYRIGHT

 Average of squared deviations from the meanSample variance:COPYRIGHT © 2013 PEARSON

© 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL
Ch.

2-

Where:

= arithmetic mean
n = sample size
Xi = ith value of the variable X


Слайд 27  
Most commonly used measure of variation in a

 Most commonly used measure of variation in a population Shows variation

population
Shows variation about the mean in a symmetric

data set
Has the same units as the original data,
Example: If original data is in meters than the standard deviation will also be in meters.


Population standard deviation:

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-


Слайд 28 Sample Standard Deviation, s
Most

Sample Standard Deviation, sMost commonly used measure of variation

commonly used measure of variation in a sample
Shows variation

about the mean
Has the same units as the original data


Sample standard deviation:

COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-


Слайд 29 Calculation Example: Sample Standard Deviation, s
COPYRIGHT ©

Calculation Example: 	Sample Standard Deviation, sCOPYRIGHT © 2013 PEARSON EDUCATION,

2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL
Ch. 2-

Sample

Data (xi) : 10 12 14 15 17 18 18 24

n = 8 Mean = x = 16


A measure of the “average” distance about the mean



Слайд 30 Class example Calculating sample variance and standard

Class example Calculating sample variance and standard deviation DR SUSANNE HANSEN SARAL

deviation
 
DR SUSANNE HANSEN SARAL


Слайд 31 Class example (continued)
 
DR SUSANNE HANSEN SARAL

Class example (continued) DR SUSANNE HANSEN SARAL

Слайд 32 Class example (continued)

The mean = 7


DR SUSANNE

Class example (continued)The mean = 7 DR SUSANNE HANSEN SARAL

HANSEN SARAL
6 8 7 10

3 5 9 8

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