Describing Data Grapically and Numerically

Overview:

This presentation aims to provide a comprehensive understanding of how to effectively describe data using both graphical and numerical methods. We will explore various techniques and tools that can help you visualize and analyze data in a meaningful and impactful way.

Key Topics:

Introduction to Data Visualization:
Importance of data visualization
Basic principles and best practices
Common data visualization tools and software
Graphical Representations:
Bar charts, histograms, and frequency distributions
Line charts and scatter plots
Pie charts and treemaps
Geographic maps and choropleths
Numerical Representations:
Measures of central tendency (mean, median, mode)
Measures of dispersion (range, variance, standard deviation)
Percentiles and quartiles  
Skewness and kurtosis

1. Chapter 2 – Book 4 Describing Data Grapically and Numerically STAT 276

2. هذه المذكرة (النوتات) عبارة عن تجميع للمعلومات من الكتاب وما تمكنت انا وزملائي من تسجيله اثناء المحاضرات. درسنا هذه المادة في اول فصل من السنة 2023-2024 و من الطبيعي ان يتغير محتوى المقرر في الفصول اللاحقة. فيجب أن: لا تعتمد على المذكرة بشكل أساسي وارجع للكتب ممكن ان تُحذف او تُضاف بعض الأشياء في الفصول اللّاحقة، فتأكد أنك تدرس ما هو مطلوب فقط معلومة مهمة: في هذا الفصل الدراسي بالتحديد يوجد هناك كتاب رئيسي للمادة، بالإضافة إلى أربع كتب أخرى. والتي يؤخذ منها بعض المعلومات، وسوف اذكر اسم الكتاب في بداية كل فصل ممكن انني أخطأت في شي ما، وسبحان من لا يخطئ. من هذا المنطلق، من واجبك كطالب، التأكد من المعلومات الموجودة في المذكرة. يوجد في آخر ( سلايد ) اسم حسابي في برنامج ( Discord )، في حال وجود أي خطأ ارجوا التواصل معي هذه المذكرة مستوحاة من (نوتات المهندس )، ألهمني عمله أن ابدأ العمل على هذه النوتات. تمنياتي لكم بالتوفيق والنجا ح

3. Table of contents 2 .1 2.3 2.2 Getting started with Statistics Frequency Distribution Tables for Qualitative & Quantitative data Classification of various types of data

4. What is Statistics ? The term statistics is commonly used in two ways. On one hand, we use it in day-to-day communication when we refer to the collection of numbers or facts. Examples On average, the starting salary of engineers is 40% higher than that of technicians In December 2009, a total of 43 states reported rising jobless rates In 2000, the salaries of CEOs from 10 selected companies ranged from $2 million to $5 million.

5. On the other hand, statistics is a scientific subject that provides the techniques of: collecting , organizing , summarizing , analyzing , and interpreting the results as input To make appropriate decisions. descriptive statistics inferential statistics. In General the subject of statistics can be divided into two parts:

6. Descriptive Statistics Descriptive statistics uses techniques to Organize , summarize , analyze , and interpret the information contained in a data set. to draw conclusions that do not go beyond the boundaries of the data set

7. Inferential Statistics uses techniques that allow us to draw conclusions about a large body of data . based on the information obtained by analyzing a small portion of these data.

8. Population and Sample in a Statistical Study 2.1. 2

9. In a very general sense, Statistics is the science of collecting and analyzing data The tradition of collecting data is old. European governments began keeping records of births, deaths and marriages four centuries ago . While techniques of analyzing data have been developed only in the twentieth century . The invention of computers made it possible to use these techniques routinely .

10. The collection and analysis of various kinds of data has become essential in these fields Agriculture Pharmaceuticals Business Medicine Engineering Manufacturing Product distribution Government or nongovernment agencies

11. A population is a collection of all elements that possess a characteristic of interest Defintion of a Population Could be finite infinite

12. A portion of a population selected for study Defintion of a Sample

13. The population we want to study Or the population about which we want to make inferences based on the information contained in a sample . Defintion of a Target Population

14. The population we took the sample from Or The population from which a sample is being selected Defintion of a Sampled population

15. Usually, the sampled population and target population coincide. But In certain situations , they may not coincide . causing conclusions to be un applicable to the target population. So, it is important to ensure the sampled population is equivalent to the target population.

16. Why would they not coincide ?

17. Financial reasons Time constraint and so forth… a part of the population not being easily accessible the unexpected loss of a part of the population

18. The problem with collecting all conceivable values of interest on all elements is that populations are usually so large that examining each element is not feasible In a typical field, there is often need to collect numerical information on all elements of interest which is usually referred to as the population .

19. examining each bulb means that we must wait until each bulb dies. Thus, it is unreasonable to collect data on all the elements of interest. Example… suppose that we are interested in determining the breaking strength of the filament in a light bulb manufactured by a particular company. Filament

20. For instance, to study family incomes in the United States, a representative sample should consist of families from different income levels . In statistical studies, the conclusions about a population are based on the information drawn from a sample So, a representative sample is crucial for studying a population, as it should possess the characteristics of the population under investigation. such as very poor , poor , middle class , rich , and very rich. A random sample is an effective approach to achieve this goal.

21. A sample is called a simple random sample if each element of the population has the same chance of being included in the sample. Defintion of a Random Sample

22. Sample Designs Also called techniques of selecting a random sample .

23. Random Sampling Simple Systematic Stratified Cluster The concept that each element of the population has the same chance of being included in a sample, forms the basis of all random sampling

24. Collecting each data point costs time and money , So it’s important to balance between sample size and resources available when taking a sample. Sample t oo small = not much useful information. Sample too large = waste of resources. Thus, it is very important that in any sampling procedure, an appropriate sampling design is selected.

25. Sampling units… Taking a sample involves dividing the target population into nonoverlapping units , known as sampling units . It's crucial to recognize that these units may not always be the same . they are determined by the chosen sample design.

26. For example , in sampling voters in a metropolitan area, the sampling units might be individual voters , all voters in a family , all voters living in a block , or all voters in a town

27. A list of all sampling units Defintion of a Sampling Frame

28. Simple Random Sampling consists of selecting a number of sampling units in such a way that each sampling unit has the same chance of being selected. Population Sample

29. Example… Simple random sampling: An engineer wants to sample machine parts manufactured during a shift at a plant. As all parts are manufactured during the same shift , it is safe to assume that all parts are representative. Hence in this case, a simple random sampling design should be appropriate..

30. Stratified Random Sampling These strata are treated as subpopulations , with similar sampling units but differing from one another The stratified random sampling design is a sampling method that divides a population into nonoverlapping groups called strata. This design offers improved results for the same amount of money spent on simple random sampling. In the manufacturing world, this type of sampling situation arises often Multiple strata are called Stratum

31. Example… Stratified random sampling: Selected samples from a population of parts manufactured in different plants or shifts can be analyzed using stratified random sampling . W hich offers administrative convenience and is more appropriate than simple random sampling. This method is particularly beneficial for machine parts manufactured in different parts of the country.

32. Stratified Random Sampling

33. Systematic Random Sampling This sampling scheme is particularly useful in manufacturing processes . When the sampling is done from a continuously operating assembly line. Under this scheme, a first item is selected randomly, then every m th item manufactured is selected until we have a sample of the desired size.

34. Systematic Random Sampling

35. Cluster Random Sampling Cluster random sampling is the fourth and final sampling design. where each unit is a group of smaller units. This is particularly useful in manufacturing environments where it is challenging to prepare a list of each part of a frame. Instead, a simple random sample of boxes with many parts can be prepared. Cluster sampling allows for a large sample of smaller units at minimum cost, as both preparing the frame and taking the sample are more economical.

36. Population Sample Cluster Random Sampling

37. A variable is a characteristic of interest that may take different values for different elements Defintion of a Variable In preparing any frame, we must precisely define the characteristic of interest or variable , where a variable may be defined as follows:

38. Example A doctor is interested in finding the ages , heights , weights , GPA , and gender of all the students in his class. Thus, the variables (characteristics of interest) are ages , heights , weights , GPA and gender حل عدل لا الشطك

39. CLASSIFICATION OF VARIOUS TYPES OF DATA 2. 2

40. This data can include: customer satisfaction employee comments employee phone numbers weekly production volume. Data collection is a common practice, often involving nonnumerical and/or numerical data. However, all data collected cannot be treated the same way due to differences in types of data. Statistical data can be divided into two major categories .

41. Quantitative Data “Numerical” Qualitative Data “Categorical” Nominal Data Ordinal Data Interval Data Ratio Data Minimum information Maximum information

42. Here is a video that explains this topic شباب ، في هذا الفيديو الدكتورة غير محجّبة (676) Nominal, Ordinal, Interval & Ratio Data: Simple Explanation With Examples - YouTube (676) Scales of Measurement - Nominal, Ordinal, Interval, & Ratio Scale Data - YouTube هذا بديل Check Page 18 of book 4 for more information and examples There are also 6 practice problems in page 19-20

43. FREQUENCY DISTRIBUTION TABLES FOR QUALITATIVE AND QUANTITATIVE DATA 2. 3

44. In statistical applications, large amounts of messy data need to be organized and summarized using a frequency distribution table. This table is used to understand the nature of qualitative or quantitative data (categorical or numerical data). This section discusses the construction of a frequency distribution table for categorial or numerical data

45. 2.3.1 Qualitative Data A frequency distribution table for qualitative data consists of two or more categories. Along with the numbers of the data that belong to each category. The number of data belonging to any category is called the frequency of that category.

46. Example… Consider a random sample of 110 small to midsize companies located in the United States and classify them according to their annual revenues (in millions of dollars). Then construct a frequency distribution table for the data obtained by this classification. We classify the annual revenues into five categories as follows: Under 250 , 250–under 500 , 500–under 750 , 750–under 1000 , 1000 or more. Then we will label each category with the numbers 1 , 2 , 3 , 4 , 5. Solution:

47. After tallying the data, we find that 28 companies belong in the first category, 26 in the second category, 20 in the third category, 16 in the fourth category, and 20 in the last category. Thus, a frequency distribution table for the data in Table 2.3.1 is as shown in Table 2.3.2

48. Interestingly we can use technology on data in Table 2.3.1 to produce Table 2.3.2

49. 2.3.2 Quantitative Data To construct a frequency distribution table for a quantitative data set , we follow the steps given below. Find number of classes “m” Find Range “R” Find class width Assign each data point to only one class and make sure to include all data points in the table

50. Range = R = largest data point − smallest data point Number of classes = m = √n where n is the total number of data points in a data set the number of classes, should always be a whole number (you must round up or down) Class width = R/m The class width should preferably be a whole number that is easy to work with. this number should be obtained only by rounding up (never by rounding down) 1 2 3

51. The frequency distribution table is prepared by assigning each data point to a class. ensuring that each data point is assigned to one class only and all data points are included in the table. The lowest class must begin with a number ≤ the smallest data point, The highest class must end with a number ≥ the largest data point in the data set.

52. Prepare a frequency distribution table for these data.

53. Solution: Range = R = 152 − 110 = 42 Number of classes = m = = 6. 3 ≈ 6 Class width = R/m = 42/6=7   The six classes used to prepare the frequency distribution table are as follows: [110–117), [117–124), [124–131), [131–138), [138–145), [145–152].

54. Each class is defined by two numbers : the lower limit and the upper limit. The upper limit does not belong to the class except for the last class. ensuring that no two classes have any common point. ensuring each data point belongs to only one class.

55. بالتوفيق Is there anything wrong in the slides ? Talk to me on Discord (I speak both English and Arabic) my username: _sayed_

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