🗊Презентация Measures of variation. Week 4 (2)

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BBA182 Applied Statistics Week 4 (2) Measures of variation Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr https://piazza.com/class/ixrj5mmox1u2t8?cid=4# www.khanacademy.org
Описание слайда:
BBA182 Applied Statistics Week 4 (2) Measures of variation Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr https://piazza.com/class/ixrj5mmox1u2t8?cid=4# www.khanacademy.org

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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.
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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.

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Using Microsoft Excel Descriptive Statistics can be obtained from Microsoft® Excel Select: data / data analysis / descriptive statistics Enter details in dialog box
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Using Microsoft Excel Descriptive Statistics can be obtained from Microsoft® Excel Select: data / data analysis / descriptive statistics Enter details in dialog box

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Using Excel to find Descriptive Statistics
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Using Excel to find Descriptive Statistics

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Using Excel to find Descriptive Statistics Enter input range details Check box for summary statistics Click OK
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Using Excel to find Descriptive Statistics Enter input range details Check box for summary statistics Click OK

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Excel output
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Excel output

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Comparing Standard Deviations of 3 different data sets
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Comparing Standard Deviations of 3 different data sets

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Measures of variation. Week 4 (2), слайд №8
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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)
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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)

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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:
Описание слайда:
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:

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Effect of the size of the standard deviation on the shape of a distribution
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Effect of the size of the standard deviation on the shape of a distribution

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Examples of applications of the standard deviation in business
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Examples of applications of the standard deviation in business

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Standard deviation a measure for risk in Finance Comparing 2 different assets, asset A and asset B with the same mean:
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Standard deviation a measure for risk in Finance Comparing 2 different assets, asset A and asset B with the same mean:

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Standard deviation a measure for consistency in quality control (Consistency in Turkish: Tutarlılık) Comparing two manufacturing processes for number of defects in a sample, with similar means of defects:
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Standard deviation a measure for consistency in quality control (Consistency in Turkish: Tutarlılık) Comparing two manufacturing processes for number of defects in a sample, with similar means of defects:

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Measuring standard deviation
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Measuring standard deviation

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Measuring standard deviation What does a standard deviation of 0 indicate? What shape will the distribution have?
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Measuring standard deviation What does a standard deviation of 0 indicate? What shape will the distribution have?

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Measuring the standard deviation Example of a data set with a standard deviation of 0: 53 53 53 53 53 53
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Measuring the standard deviation Example of a data set with a standard deviation of 0: 53 53 53 53 53 53

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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)
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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)

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Effect of outliers on Variance and standard deviation A large outlier (negative or positive) will increase the variance and standard deviation
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Effect of outliers on Variance and standard deviation A large outlier (negative or positive) will increase the variance and standard deviation

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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.
Описание слайда:
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.

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Which iron is more consistent? The current or the newly developed? Excel output:
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Which iron is more consistent? The current or the newly developed? Excel output:

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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.
Описание слайда:
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.

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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.
Описание слайда:
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.

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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
Описание слайда:
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

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Coefficient of Variation (CV) Comparing 2 different production processes with different means: Process 1 Process 2 18 18 19 35 15 12 18 19 17 16 87/ 5 = 17.4 100/5 = = 20 s = 1.51 s = 8.80
Описание слайда:
Coefficient of Variation (CV) Comparing 2 different production processes with different means: Process 1 Process 2 18 18 19 35 15 12 18 19 17 16 87/ 5 = 17.4 100/5 = = 20 s = 1.51 s = 8.80

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Coefficient of Variation (CV) Process 1: Process 2: 87/ 5 = 17.4 100/5 = = 20 s = 1.51 s = 8.80 = x 100 % = 0.086 x 100% = 8.68% CV = = 0.44 x 100% = 44 %
Описание слайда:
Coefficient of Variation (CV) Process 1: Process 2: 87/ 5 = 17.4 100/5 = = 20 s = 1.51 s = 8.80 = x 100 % = 0.086 x 100% = 8.68% CV = = 0.44 x 100% = 44 %

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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
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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

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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
Описание слайда:
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

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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.
Описание слайда:
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.

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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 %.
Описание слайда:
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 %.

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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.
Описание слайда:
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.

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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?
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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?

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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.
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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.

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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?
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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?

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Class quizz Comparing the variation/ spread in two different processes: Standard deviation and Coefficient of variation: (1) In which situation will we use the standard deviation as the measure of variation? (2) In which situations will we need to use the Coefficient of variation?
Описание слайда:
Class quizz Comparing the variation/ spread in two different processes: Standard deviation and Coefficient of variation: (1) In which situation will we use the standard deviation as the measure of variation? (2) In which situations will we need to use the Coefficient of variation?

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