Measures of variation. Week 4 (2)

Сентябрь 14, 2022

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Measures of variation. Week 4 (2)

Содержание

2. Average distance to the mean: Standard deviation Most commonly used measure of variability Measures the standard
3. Using Microsoft Excel Descriptive Statistics can be obtained from Microsoft® Excel Select: data / data analysis
4. Using Excel to find Descriptive Statistics COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL
5. Using Excel to find Descriptive Statistics Enter input range details Check box for summary statistics Click
6. Excel output COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL Ch. 2- Microsoft Excel
7. Comparing Standard Deviations of 3 different data sets COPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS
8. DR SUSANNE HANSEN SARAL 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120 Comparing Standard Deviations of 2 data sets Without calculating, which
9. Describing distributions – what to pay attention to! Pay attention to: its’ shape (symmetric, right or
10. Effect of the size of the standard deviation on the shape of a distribution The standard
11. Effect of the size of the standard deviation on the shape of a distribution COPYRIGHT ©
12. Examples of applications of the standard deviation in business Logistics: Measurement of timeliness/reliability/consistency Financial sector: Measurement
13. Standard deviation a measure for risk in Finance DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR Comparing 2 different
14. Standard deviation a measure for consistency in quality control (Consistency in Turkish: Tutarlılık) DR SUSANNE HANSEN
15. Measuring standard deviation DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR Small standard deviation Low risk/high consistency Large standard
16. Measuring standard deviation What does a standard deviation of 0 indicate? What shape will the distribution
17. Measuring the standard deviation Example of a data set with a standard deviation of 0: 53
18. Advantages of Variance and Standard Deviation Each single value in the data set is used in
19. Effect of outliers on Variance and standard deviation A large outlier (negative or positive) will increase
20. Comparing the consistency of two types of Golf clubs Golf equipment manufacturers are constantly seeking ways
21. Which iron is more consistent? The current or the newly developed? Excel output: COPYRIGHT © 2013
22. Interpretation of the data (golf club) The standard deviation of the distances of the current iron
23. Coefficient of Variation (CV) In situations where the means are almost the same, it is appropriate
24. Coefficient of Variation (CV) Measures relative variation within a dataset Always in percentage (%) 0 –
25. Coefficient of Variation (CV) DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR
26. Coefficient of Variation (CV) DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR
27. Comparing Coefficient of Variation Stock A: Average price last year = $ 4.00 Standard deviation =
28. Comparing Coefficient of Variation Stock A: Average price last year = $ 4.00 Standard deviation =
29. Comparing Coefficient of Variation, (CV) The standard deviation of stock A, is $2, and that of
30. When to use Standard deviation and coefficient of variation, when comparing two data sets Use Standard
31. Standard deviation and coefficient of variation – measures of variation The standard deviation is the average
32. Application of coefficient of variation, CV With the following information about investment A: Can we say
33. Application of coefficient of variation (continued) With the coefficient of variation we can analyze the relative
34. Class quizz What is the median? What does the Range measure? What does IQR measure? How
36. Скачать презентацию

Слайд 2

Average distance to the mean: Standard deviation
Most commonly used measure

of variability
Measures the standard (average) distance of all data points from the mean.

2/23/2017

Слайд 3

Using Microsoft Excel
Descriptive Statistics can be obtained from Microsoft® Excel
Select: data /

data analysis / descriptive statistics
Enter details in dialog box

Ch. 2-

Слайд 4

Using Excel to find Descriptive Statistics
COPYRIGHT © 2013 PEARSON EDUCATION, INC.

PUBLISHING AS PRENTICE HALL

Ch. 2-

Select data / data analysis / descriptive statistics

Слайд 5

Using Excel to find Descriptive Statistics
Enter input range details
Check box

for summary statistics
Click OK

Ch. 2-

Слайд 6

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

Microsoft Excel
descriptive statistics output,
using the house price data:

House Prices: $2,000,000
500,000 300,000 100,000 100,000

Слайд 7

Comparing Standard Deviations of 3 different data sets
COPYRIGHT © 2013

PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALL

Ch. 2-

s = 3.338
(compare to the two cases below)

11 12 13 14 15 16 17 18 19 20 21

Data B

Data A

s = 0.926
(values are concentrated near the mean)

11 12 13 14 15 16 17 18 19 20 21

s = 4.570
(values are dispersed far from the mean)

Data C

Mean = 15.5 for each data set

Слайд 8

DR SUSANNE HANSEN SARAL
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120
Comparing Standard Deviations of 2 data sets
Without

calculating, which of the two data sets do you expect to have the highest variation and standard deviation? Why?

Слайд 9

Describing distributions – what to pay attention to!
Pay attention to:
its’

shape (symmetric, right or left skewed)
its’ center (mean, median, mode)
Its’ spread (variance, standard deviation)

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@GMAIL.COM

Слайд 10

Effect of the size of the standard deviation on the

shape of a distribution
The standard deviation affects the shape of a distribution:
When there are small distances between the data points, most of the scores in the data set will be close to the mean and the resulting standard deviation will be small. The distribution will be narrow.
When there are large distances between data points, the scores will be further away from the mean and the standard deviation is larger. The distribution will be wide.
As illustrated in the following slide:

Ch. 2-

Слайд 11

Effect of the size of the standard deviation on the shape

of a distribution

Ch. 2-

Small standard deviation-the mean
represents the data well
Large standard deviation – mean
a bad representation of the data

Слайд 12

Examples of applications of the standard deviation in business
Logistics:
Measurement

of timeliness/reliability/consistency
Financial sector:
Measurement of risk (difference between actual rate of
return and the expected rate of return)
Production:
Quality control management. Measurement of consistency and
reliability of manufacturing processes

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 13

Standard deviation a measure for risk in Finance
DR SUSANNE HANSEN

SARAL, SUSANNE.SARAL@OKAN.EDU.TR
Comparing 2 different assets, asset A and asset B with the same mean:

Слайд 14

Standard deviation a measure for consistency in quality control (Consistency

in Turkish: Tutarlılık)

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR
Comparing two manufacturing processes for number of defects in a sample, with similar means of defects:

Слайд 15

Measuring standard deviation
DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR
Small standard deviation
Low risk/high

consistency
Large standard deviation
High risk/low consistency

Слайд 16

Measuring standard deviation
What does a standard deviation of 0

indicate?
What shape will the distribution have?

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 17

Measuring the standard deviation
Example of a data set with

a standard deviation of 0:
53 53 53 53 53 53

Слайд 18

Advantages of Variance and Standard Deviation
Each single value in the data

set is used in the calculation
Values far from the mean are given extra weight, such as outliers
(because deviations from the mean are squared)

Ch. 2-

Слайд 19

Effect of outliers on Variance and standard deviation
A large outlier

(negative or positive) will increase the variance and
standard deviation

Слайд 20

Comparing the consistency of two types of Golf clubs
Golf equipment

manufacturers are constantly seeking ways to improve their products. Suppose that the R&D department has developed a new golf iron (7-iron) to improve the consistency of its users.
A test golfer was asked to hit 150 shots using a 7-iron, 75 of which were hit with his current club and 75 with the newly developed 7-iron.
The distances were then measured and recorded.

Ch. 2-

Слайд 21

Which iron is more consistent? The current or the newly

developed? Excel output:

Ch. 2-

Слайд 22

Interpretation of the data (golf club)
The standard deviation of the distances

of the current iron is 5.79 meters whereas that of the newly developed 7-iron is 3.09 meters.
Based on this sample, the newly developed iron is more consistent (there is less variation in the distances shot with the innovative golf club).
Because the mean distances are similar it would appear that the new 7-iron is indeed superior.

Ch. 2-

Слайд 23

Coefficient of Variation (CV)
In situations where the means are almost the

same, it is appropriate to use the standard deviations to see which process is the most consistent.
In situations where the means are different we need to calculate the coefficient of variation to compare the consistency or riskiness.
The coefficient of variation expresses the standard deviation as a percentage of the mean.

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 24

Coefficient of Variation (CV)
Measures relative variation within a dataset
Always

in percentage (%) 0 – 100
A low CV translates into low variation within the same data set, a high CV into high variation

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Population coefficient of variation (CV):

Sample coefficient of variation (CV):

Слайд 25

Coefficient of Variation (CV)

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 26

Coefficient of Variation (CV)

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 27

Comparing Coefficient of Variation
Stock A:
Average price last year = $

4.00
Standard deviation = $ 2.00
Stock B:
Average price last year = $ 80.00
Standard deviation = $ 8.00

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Note: The standard deviation for stock A is lower than the standard deviation for stock B.

Слайд 28

Comparing Coefficient of Variation
Stock A:
Average price last year = $

4.00
Standard deviation = $ 2.00
Stock B:
Average price last year = $ 80.00
Standard deviation = $ 8.00

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Note: The standard deviation for stock A is lower than the standard deviation for stock B.

Слайд 29

Comparing Coefficient of Variation, (CV)
The standard deviation of stock A,

is $2, and that of stock B, is $ 8, we would believe that stock B is more volatile or risky.
However, the average closing price for stock A is $ 4, and $ 80 for stock B.
The CV of stock A is higher, 50%, meaning that the market value of the stock fluctuates more from period to period than does that of stock B, 10%.
Therefore, a lower CV indicates lower riskiness in finance and higher precision or consistency in a production process.

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 30

When to use Standard deviation and coefficient of variation, when

comparing two data sets
Use Standard deviation, SD, as a measure of risk/ consistency/reliability when comparing two or more objects:
Means are identical or very close
Use Coefficient of variation, CV, as a measure of risk/ consistency/reliability when comparing two or more objects:
Means are different
The coefficient of variation, CV, expresses the standard deviation as a percentage of it’s mean. Is measured between 0 – 100 %.

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 31

Standard deviation and coefficient of variation – measures of variation
The

standard deviation is the average distance of all the scores within a distribution around the mean.
The coefficient of variation is the standard deviation relative (in percent) to its’ mean.
We can use the coefficient of variation to determine the relative variance within one particular process.

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 32

Application of coefficient of variation, CV
With the following information about investment

A:
Can we say what risk it carries? Is this a high or low risk?

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 33

Application of coefficient of variation (continued)
With the coefficient of variation we

can analyze the relative variation (in percent) around the mean:
The coefficient of variation tells us that for investment A the sample standard deviation is 42.2 % from the mean.

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Слайд 34

Class quizz
What is the median?
What does the Range measure?

What does IQR measure?
How do we illustrate categorical data?
Why do we collect a sample from the population?
What are data?
What types of data do we work with in statistics?

Measures of variation. Week 4 (2)

Содержание

Average distance to the mean: Standard deviationMost commonly used measure

Using Microsoft ExcelDescriptive Statistics can be obtained from Microsoft® ExcelSelect: data /

Using Excel to find Descriptive StatisticsCOPYRIGHT © 2013 PEARSON EDUCATION, INC.

Using Excel to find Descriptive StatisticsEnter input range detailsCheck box

Excel outputCOPYRIGHT © 2013 PEARSON EDUCATION, INC. PUBLISHING AS PRENTICE HALLCh.

Comparing Standard Deviations of 3 different data setsCOPYRIGHT © 2013

DR SUSANNE HANSEN SARAL 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120Comparing Standard Deviations of 2 data setsWithout

Describing distributions – what to pay attention to!Pay attention to: its’

Effect of the size of the standard deviation on the

Effect of the size of the standard deviation on the shape

Examples of applications of the standard deviation in businessLogistics: Measurement

Standard deviation a measure for risk in FinanceDR SUSANNE HANSEN

Standard deviation a measure for consistency in quality control (Consistency

Measuring standard deviationDR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TRSmall standard deviationLow risk/high

Measuring standard deviation What does a standard deviation of 0

Measuring the standard deviation Example of a data set with

Advantages of Variance and Standard DeviationEach single value in the data

Effect of outliers on Variance and standard deviation A large outlier

Comparing the consistency of two types of Golf clubsGolf equipment

Which iron is more consistent? The current or the newly

Interpretation of the data (golf club)The standard deviation of the distances

Coefficient of Variation (CV)In situations where the means are almost the

Coefficient of Variation (CV)Measures relative variation within a dataset Always

Coefficient of Variation (CV) DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Coefficient of Variation (CV) DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Comparing Coefficient of VariationStock A:Average price last year = $

Comparing Coefficient of VariationStock A:Average price last year = $

Comparing Coefficient of Variation, (CV) The standard deviation of stock A,

When to use Standard deviation and coefficient of variation, when

Standard deviation and coefficient of variation – measures of variationThe

Application of coefficient of variation, CVWith the following information about investment

Application of coefficient of variation (continued)With the coefficient of variation we

Class quizz What is the median? What does the Range measure?

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Descriptive Statistics can be obtained from Microsoft® Excel
Select: data /

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COPYRIGHT © 2013 PEARSON EDUCATION, INC.

Using Excel to find Descriptive Statistics
Enter input range details
Check box

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

Comparing Standard Deviations of 3 different data sets
COPYRIGHT © 2013

DR SUSANNE HANSEN SARAL
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5
1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120
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its’

Examples of applications of the standard deviation in business
Logistics:
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DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR
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What does a standard deviation of 0

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Example of a data set with

Advantages of Variance and Standard Deviation
Each single value in the data

Effect of outliers on Variance and standard deviation
A large outlier

Comparing the consistency of two types of Golf clubs
Golf equipment

Interpretation of the data (golf club)
The standard deviation of the distances

Coefficient of Variation (CV)
In situations where the means are almost the

Coefficient of Variation (CV)
Measures relative variation within a dataset
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DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Coefficient of Variation (CV)

DR SUSANNE HANSEN SARAL, SUSANNE.SARAL@OKAN.EDU.TR

Comparing Coefficient of Variation
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Average price last year = $

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Stock A:
Average price last year = $

Comparing Coefficient of Variation, (CV)
The standard deviation of stock A,

Standard deviation and coefficient of variation – measures of variation
The

Application of coefficient of variation, CV
With the following information about investment

Application of coefficient of variation (continued)
With the coefficient of variation we

Class quizz
What is the median?
What does the Range measure?