1. Stat 101Dr SaMeH1 Statistics (Stat 101) Associate Professor of Environmental Eng. Civil Engineering Department Engineering College Almajma’ah University smohamed1@ksu.edu.sa http://faculty.ksu.edu.sa/SaMeH 2010/2011 Sameh Saadeldin Ahmed

2. Chapter 1 WeekSubjectContent 1 st week Concepts of Probability and Statistics What is Statistics? Types of Statistics Basic Terms Types of Variables Sources of Data Data Collection Approaches Stat 101Dr SaMeH2

3. Contents (week by week) WeekSubjectContent 2 nd week Organizing Data Organizing and Graphing Qualitative Data Organizing and Graphing Quantitative Data 3 rd week Shapes of Histograms Histogram, Polygon, Frequency Curve Cumulative Frequency Distributions Stat101Dr SaMeH3

4. Stat 101Dr SaMeH4 Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data 2.1Raw Data Example 2.1: Table 2.1 gives a quantitative raw data for the ages of 50 students selected from a college.

5. Tables 2.1 and 2.2: Age and Grades of 50 students Stat 101Dr SaMeH5 21192425293426273733 1820192219 25222523 25193119231823192326 2228212022 21201921 CABDCCDCCC AACAAADBDC CADBBACADD BDCBBCCBAB

6. 2.2 Organizing and Graphing Qualitative Data Data sets are organized into tables, and data are displayed using graphs. Stat 101Dr SaMeH6 2.2.1 Frequency Distribution A frequency distribution exhibits how the frequencies are distributed over various categories.

7. Tables 2.3 : Grads of 60 Students in Math 105 Stat 101Dr SaMeH7 DBECDBDCEA BECDBDDAEC CDACEDCCDB DEDDADDCDC DABDBDCDCE DBCCEDCCDA Example 2.2: Table 2.3 shows the grades of 60 students in Math 105. It is required to summarise the data in a table form.

8. Solution Stat 101Dr SaMeH8 Type (grade) TallyFrequency (f) A//// /6 B8 C16 D22 E8 SUM60 Type (grade)Frequency (f) A6 B8 C16 D22 E8 SUM60 frequency Category

9. Stat 101Dr SaMeH9 Frequency Distribution for Qualitative Data A frequency distribution for qualitative data lists all categories and the number of elements that belong to each of the category.

10. 2.2 Organizing and Graphing Qualitative Data Stat 101Dr SaMeH10 2.2.1 Frequency Distribution 2.2.1 Frequency Distribution A relative frequency of a category is obtained by dividing the frequency of that category by the sum of all frequencies.  2.2.2 Relative Frequency & Percentage

11. Stat 101Dr SaMeH11 Calculating Relative Frequency of a Category Relative frequency of a category = frequency of that category / sum of all frequencies Calculating Percentage Percentage = (Relative frequency) x 100

12. Stat 101Dr SaMeH12 Example 2.3: Determine the relative frequency and percentage distributions for the data in Table 2.3 Solution: TypeFrequency (f) Relative Frequency Percentage A66/60 = 0.10.1 (100) = 10 B88/60 = 0.13330.133 (100) = 13.3 C1616/60 = 0.2660.266 (100) = 26.6 D2222/60 = 0.3660.366 (100) = 36.6 E88/60 = 0.1330.133 (100) = 13.3 SUM601.00100

13. Stat 101Dr SaMeH13 Example 2.4: The following data represents the marks of 50 students in a subject 51957074739071749067 91728389508072848569 62828776917687757879 71968188648273578670 You are required to: Construct a table shows grade distribution of the student’s grades. A table shows the frequency distribution of the student’s marks. A table shows the relative distribution of the student’s marks. A table shows the percentage frequency distribution of the student’s marks.

14. Stat 101Dr SaMeH14 Solution 1- A table shows the distribution of the student’s grades CategoryTallyFrequency 50 – 59///3 60 – 695 70 – 7918 80 – 8916 90 - 998 SUM50 2- A table show the Frequency distribution of the student’s marks CategoryFrequency 50 – 593 60 – 695 70 – 7918 80 – 8916 90 - 998 SUM50

15. Stat 101Dr SaMeH15 3- A table shows the relative distribution of the student’s marks CategoryFrequency (f)Relative Frequency 50 – 5933/50 = 0.06 60 – 6955/50 = 0.10 70 – 791818/50 = 0.36 80 – 891616/50 = 0.32 90 - 9988/50 = 0.16 SUM501.00

16. Stat 101Dr SaMeH16 4- A table shows the percentage frequency distribution of the student’s marks. CategoryFrequency (f) Relative Frequency 50 – 5933/50 = 0.06 60 – 6955/50 = 0.10 70 – 791818/50 = 0.36 80 – 891616/50 = 0.32 90 - 9988/50 = 0.16 SUM501.00 Percentage 0.06 (100) = 6 0.10 (100) = 10 0.36 (100) = 36 0.32 (100) = 32 0.16 (100) = 16 100

17. 2.2 Organizing and Graphing Qualitative Data Stat 101Dr SaMeH17 2.2.1 Frequency Distribution 2.2.1 Frequency Distribution Bar Graphs Pie Chart. 2.2.2 Relative Frequency & Percentage 2.2.2 Relative Frequency & Percentage 2.2.3 Graphical Presentation of Qualitative

18. Stat 101Dr SaMeH18 Bar Graphs To construct the bar graph or bar chart, we mark the various categories on the horizontal axis (all categories are represented by intervals of the same width). The frequencies are presented on the vertical axis. The height of the bar represents the frequency of the corresponding category.

19. Stat 101Dr SaMeH19 The bar graphs for the relative frequency and percentage distributions can be drawn by making the relative frequencies or percentages, instead of the class frequencies on the vertical axis.

20. Stat 101Dr SaMeH20 Pie Chart A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories.

21. 2.3 Organizing and Graphing Quantitative Data Stat 101Dr SaMeH21 2.3.1 Frequency Distribution Table 2.4 gives the weekly earnings of 100 employees of a large company. The first column lists the classes, which represent the (quantitative) variable weekly earnings. For quantitative data, an interval that includes all the values that falls within two numbers. The lower and upper limits, is called a class. Note that the classes always represent a variable. The second column lists the number of employees who have earnings within each class (frequency).

22. Stat 101Dr SaMeH22 Table 2.4: Weekly earnings of 100 employees of a company variable Weekly earnings (dollars) Number of employees (f) 401 to 6009 601 to 80022 801 to 100039 1001 to 120015 1201 to 14009 1401 to 16006 Second Class Upper Limit Frequency of Third class Lower Limit

23. Stat 101Dr SaMeH23 Frequency Distribution for Quantitative Data A frequency distribution for quantitative data lists all classes and the number of values that belong to each class. Data in the form of a frequency distribution are called grouped data. To find the midpoint of the upper limit of the first class and the lower limit of the second class in Table 2.4, we divide the sum of these two limits by 2. Thus, this midpoint is [600 + 601] / 2 = 600.5 The value 600.5 is called the upper boundary of the first class and the lower boundary of the second class.

24. Stat 101Dr SaMeH24 Class Boundary The class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class. We can convert the class limits of table 2.4 to class boundaries, which are also called real class limits. The second column of table 2.5 lists the boundaries for table 2.4.

25. Stat 101Dr SaMeH25 Table 2.5: Class boundaries, Class widths, and Class midpoints for Table 2.4 Class LimitsClass boundariesClass width Class Midpoint 401 to 600400.5 to less than 600.5200500.5 601 to 800600.5 to less than 800.5200700.5 801 to 1000800.5 to less than 1000.5200900.5 1001 to 12001000.5 to less than 1200.52001100.5 1201 to 14001200.5 to less than 1400.52001300.5 1401 to 16001400.5 to less than 1600.52001500.5 The difference between the two boundaries of a class gives the class width. The class width is called the class size.

26. Stat 101Dr SaMeH26 Finding Class Width Class width = Upper boundary – Lower boundary Calculating Class Midpoint or Mark Class midpoint or mark = [Lower limit + Upper limit] / 2 The class midpoint or mark is obtained by dividing the sum of the two limits (or the two boundaries) of a class by 2. Thus the midpoint of the first class in Table 2.4 or Table 2.5 is calculated as follows : Midpoint of the first class = [401 + 600] / 2 = 500.5

27. Stat 101Dr SaMeH27 Example 2.5: Use the data given in example 2.4 to calculate the class limits, class boundaries, midpoints and list the calculated relative frequencies and percentage, all in one table. A table shows all the above and the class midpoint. Solution: Class Limits Class Boundaries Class Midpoint Frequency f Relative Frequency Percentage 50 – 5949.5 – 59.554.530.066 60 – 6959.5 – 69.564.550.1010 70 – 7969.5 – 79.574.5180.3636 80 – 8979.5 – 89.584.5160.3232 90 – 9989.5 – 99.594.580.1616 SUM501.00100

28. End of Part 3 Get ready for a quiz (2)…… next lecture!! Stat 101Dr SaMeH28