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Слайды и текст к этой презентации:

№1 слайд
BBA Applied Statistics Week
Содержание 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
№2 слайд
Average distance to the mean
Содержание слайда: 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.
№3 слайд
Using Microsoft Excel
Содержание слайда: Using Microsoft Excel Descriptive Statistics can be obtained from Microsoft® Excel Select: data / data analysis / descriptive statistics Enter details in dialog box
№4 слайд
Using Excel to find
Содержание слайда: Using Excel to find Descriptive Statistics
№5 слайд
Using Excel to find
Содержание слайда: Using Excel to find Descriptive Statistics Enter input range details Check box for summary statistics Click OK
№6 слайд
Excel output
Содержание слайда: Excel output
№7 слайд
Comparing Standard Deviations
Содержание слайда: Comparing Standard Deviations of 3 different data sets
№8 слайд
Содержание слайда:
№9 слайд
Describing distributions what
Содержание слайда: 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)
№10 слайд
Effect of the size of the
Содержание 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:
№11 слайд
Effect of the size of the
Содержание слайда: Effect of the size of the standard deviation on the shape of a distribution
№12 слайд
Examples of applications of
Содержание слайда: Examples of applications of the standard deviation in business
№13 слайд
Standard deviation a measure
Содержание слайда: Standard deviation a measure for risk in Finance Comparing 2 different assets, asset A and asset B with the same mean:
№14 слайд
Standard deviation a measure
Содержание слайда: 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:
№15 слайд
Measuring standard deviation
Содержание слайда: Measuring standard deviation
№16 слайд
Measuring standard deviation
Содержание слайда: Measuring standard deviation What does a standard deviation of 0 indicate? What shape will the distribution have?
№17 слайд
Measuring the standard
Содержание слайда: Measuring the standard deviation Example of a data set with a standard deviation of 0: 53 53 53 53 53 53
№18 слайд
Advantages of Variance and
Содержание слайда: 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)
№19 слайд
Effect of outliers on
Содержание слайда: Effect of outliers on Variance and standard deviation A large outlier (negative or positive) will increase the variance and standard deviation
№20 слайд
Comparing the consistency of
Содержание 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.
№21 слайд
Which iron is more
Содержание слайда: Which iron is more consistent? The current or the newly developed? Excel output:
№22 слайд
Interpretation of the data
Содержание 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.
№23 слайд
Coefficient of Variation CV
Содержание 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.
№24 слайд
Coefficient of Variation CV
Содержание 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
№25 слайд
Coefficient of Variation CV
Содержание 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
№26 слайд
Coefficient of Variation CV
Содержание 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 %
№27 слайд
Comparing Coefficient of
Содержание 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
№28 слайд
Comparing Coefficient of
Содержание 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
№29 слайд
Comparing Coefficient of
Содержание 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.
№30 слайд
When to use Standard
Содержание 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 %.
№31 слайд
Standard deviation and
Содержание 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.
№32 слайд
Application of coefficient of
Содержание слайда: 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?
№33 слайд
Application of coefficient of
Содержание слайда: 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.
№34 слайд
Class quizz What is the
Содержание слайда: 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?
№35 слайд
Class quizz Comparing the
Содержание 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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