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13/14 Semester 1 Computer Programming (TKK-2144) Instructor: Rama Oktavian Email: [email protected]) Office Hr.: T.12-14, Th. 12-14 Outlines 1. Statistical calculation (theory) 2. Statistical calculation (exercise) Statistics Statistics: Basic Ideas Statistics is the area of science that deals with collection, organization, analysis, and interpretation of data. It also deals with methods and techniques that can be used to draw conclusions about the characteristics of a large number of data points-commonly called a population-By using a smaller subset of the entire data. Statistics Statistics in Engineering Engineers apply physical and chemical laws and mathematics to design, develop, test, and supervise various products and services. Engineers perform tests to learn how things behave under stress, and at what point they might fail. Statistics Statistics in Engineering As engineers perform experiments, they collect data that can be used to explain relationships better and to reveal information about the quality of products and services they provide. Statistical method Statistics Statistics in Chemical Engineering Why?? Statistical methods of data analysis are valuable tools to chemical engineers in both research and in industrial practice. Statistics Statistics in Chemical Engineering Example - Reliable and reproducible the temperature measurements?? - Temperature variation?? - Draw a conclusion Statistics Basic terms in Statistics Population Any entire collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to describe or draw conclusions about. Sample A group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the larger group. Statistics Basic terms in Statistics calculation Mean (AVERAGE): The sum of all samples divided by the number of values n x x i 1 n Median (MEDIAN): the middle value of a set of data containing an odd number of values, or the average of the two middle values of a set of data with an even number of values. For example, to find the median of {9, 3, 6, 7, 5}, we first sort the data giving {3, 5, 6, 7, 9}, then choose the middle value 6. If the number of observations is even, e.g., {9, 3, 6, 7, 5, 2}, then the median is the average of the two middle values from the sorted sequence, in this case, (5 + 6) / 2 = 5.5. Mode : The value that is observed most frequently. The mode is undefined for sequences in which no observation is repeated. Statistics Methods of Variability Measurement Variability (or dispersion) measures the amount of scatter in a dataset. Commonly used methods: range, variance, standard deviation, interquartile range, coefficient of variation etc. Range: The difference between the largest and the smallest observations. The range of 10, 5, 2, 100 is (100-2)=98. It’s a crude measure of variability. Statistics Methods of Variability Measurement Standard Deviation: It gives an idea of how close the entire set of data is to the average value. Data sets with a small standard deviation have tightly grouped, precise data. Data sets with large standard deviations have data spread out over a wide range of values. s 2 x x i n 1 Sample variance (VAR): Square of the standard deviation: n s2 x x 2 i 1 n 1 Outliers are values xi which differ significantly from the mean Statistics (Exercise) How to access statistical functions in Excel 2007 Instead of using the menu, you can type in the functions. So, =average(b2:b16) finds the mean of the values in cells b2 thru b16. Statistics (Exercise) How to access statistical functions in Excel 2007 Descriptive Statistics – “Location” Mean (average) – Strongly affected by unusual points – =average(b2:b28) Median (50% of data higher, 50% of data lower) – Seldom strongly affected by unusual points – =median(b2:b28) Statistics (Exercise) How to access statistical functions in Excel 2007 Descriptive Statistics – “Variability” Standard Deviation, =stdev(b2:b28) – A measure of how widely the data is spread around the mean – Strongly affected by unusual points Relative Standard Deviation – =stdev(b2:b28)/average(b2:b28) – Usually given as percentage Format > Cells > Percent Variance – =(stdev(b2:b28))^2 – =Var (b2:b28) Statistics (Exercise) How to access statistical functions in Excel 2007 Population Mean Statistics (Exercise) How to access statistical functions in Excel 2007 Summarizing Data Try out the various descriptive statistics to summarize the “location” and “variability” of the data To summarize the data, we need more statistics power. To get more statistics power from Excel, you need to add in the Analysis ToolPak Statistics (Exercise) How to access statistical functions in Excel 2007 Add in the Analysis ToolPak Click the Microsoft Office button, then Excel Options. Statistics (Exercise) How to access statistical functions in Excel 2007 Add in the Analysis ToolPak Click Add ins. In the “Manage” box, select Excel Add ins. Click “Go” Statistics (Exercise) Add in the Analysis ToolPak • Click the checkbox for the Analysis ToolPak, then ‘OK’ • Install it if it isn’t installed • When you have added it in, it will appear on the ‘Data’ page Statistics (Exercise) Add in the Analysis ToolPak Optional method: •Select Data •Select Data Analysis •Select Descriptive Statistics from the next dialog box Statistics (Exercise) Add in the Analysis ToolPak Statistics (Exercise) Add in the Analysis ToolPak