Chapter 2 business mathematics for .pptx

mathematics

1. STATISTICS & DATA REPRESENTATION

2. What is Statistics Statistics is a science that involves the use of numerical data. It can be defined as “science of collecting, organizing, presenting, analyzing, and interpreting numerical data to help in process of making decisions The profession that involve statistics is called a “statistician”. Statistics use in marketing, accounting, quality control, and others.

3. Why study Statistics? Data are everywhere Statistical techniques are used to make many decisions that affect our lives No matter what your career, you will make professional decisions that involve data. An understanding of statistical methods will help you make these decisions efectively

4. Applications of statistical concepts in the business world Finance – correlation and regression, index numbers, time series analysis Marketing – hypothesis testing, chi- square tests, nonparametric statistics Personel – hypothesis testing, chi- square tests, nonparametric tests Operating management – hypothesis testing, estimation, analysis of variance, time series analysis

5. Types of Statistics There are 2 types of statistics; descriptive statistics inferential statistics.

6. Descriptive Statistics Describe the sample data (basic features) Provide simple summaries about data and the measures together with graphical analysis. Definition: organizing, presenting, and analyzing numerical data. Used to present quantitative description in manageable form.

7. Inferential Statistics Involves using a sample to draw conclusions about a population. Estimation e.g., Estimate the population mean weight using the sample mean weight Hypothesis testing e.g., Test the claim that the population mean weight is 70 kg Inference is the process of drawing conclusions or making decisions about a population based on sample results

8. Term in Statistics Data consists of information coming from observations, counts, measurements, or responses. A population is the collection of all outcomes, responses, measurement, or counts that are of interest. A sample is a subset of a population.

9. Parameter & Statistics A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. Parameter Population Statistic Sample

10. Data Statistical data are usually obtained by counting or measuring items. Most data can be put into the following categories: Qualitative - data are measurements that each fail into one of several categories. (hair color, ethnic groups and other attributes of the population) quantitative - data are observations that are measured on a numerical scale (distance traveled to college, number of children in a family, etc.)

11. Qualitative Data Qualitative data are generally described by words or letters. They are not as widely used as quantitative data because many numerical techniques do not apply to the qualitative data. For example, it does not make sense to find an average hair color or blood type. Qualitative data can be separated into two subgroups: dichotomic (if it takes the form of a word with two options (gender - male or female) polynomic (if it takes the form of a word with more than two options (education - primary school, secondary school and university).

12. Quantitative Data Quantitative data are always numbers and are the result of counting or measuring attributes of a population. Quantitative data can be separated into two subgroups: discrete (if it is the result of counting (the number of students of a given ethnic group in a class, the number of books on a shelf, ...) continuous (if it is the result of measuring (distance traveled, weight of luggage, …)

13. Type of Data Data sets can consist of two types of data: qualitative data and quantitative data Data Qualitative Data Quantitative Data Consists of attributes, labels, or non- numerical entries. Consists of numerical measurements or counts.

14. Types of variables Variables Quantitative Qualitative Dichotomic Polynomic Discrete Continuous Gender, marital status Brand of Pc, hair color Children in family, Strokes on a golf hole Amount of income tax paid, weight of a student

15. Level of Measurement The level of measurement determines which statistical calculations are meaningful. The four levels of measurement are: nominal , ordinal , interval , and ratio . Nominal Levels of Measurement Ordinal Interval Ratio Lowest to highest

16. Nominal Level Data at the nominal level of measurement are qualitative only. Levels of Measurement Nominal Calculated using names, labels, or qualities. No mathematical computations can be made at this level. Colors in the Malaysia flag Names of students in your class Textbooks you are using this semester

17. Ordinal Level Data at the ordinal level of measurement are qualitative or quantitative. Levels of Measurement Class standings: freshman, sophomore, junior, senior Numbers on the back of each player’s shirt Ordinal Arranged in order, but differences between data entries are not meaningful. Top 50 songs played on the radio

18. Interval Level Data at the interval level of measurement are quantitative. A zero entry simply represents a position on a scale; the entry is not an inherent zero. Levels of Measurement Temperatures Years on a timeline Interval Arranged in order, the differences between data entries can be calculated. Size of shoes

19. Ratio Level Data at the ratio level of measurement are similar to the interval level, but a zero entry is meaningful. Levels of Measurement A ratio of two data values can be formed so one data value can be expressed as a ratio. Ratio Ages Grade point averages Weights

20. Summary of Levels of Measurement Level of measurement Put data in categories Arrange data in order Subtract data values Determine if one data value is a multiple of another Nominal Yes No No No Ordinal Yes Yes No No Interval Yes Yes Yes No Ratio Yes Yes Yes Yes

21. Source of Data There are two source of data Primary data Secondary data

22. Primary Data Specific information collected by the person who is doing the research Data collect through survey, interviews, direct observations and experiment. Example: Population Census Advantage: High Respond rate Accurate Disadvantage 1. Lot of time consuming, effort, and cost

23. Secondary Data Data that has been collected form other parties. Eg. Journals, yearly report etc. Easily available Advantage Convenient and less time effort, and cost Disadvantage Produce error May not meet specific needs

24. Presentation of Data “Method by which the people organize, summarize and communicate information using a variety of tools such as tables, graphs, and diagram.

25. Uses of Presentation Easy and better understanding of the subject Provides first hand information about data Helpful in future analysis Easy for making comparisons Very attractive

26. Tabulation It is a systematic and logical arrangement of classified data in rows and columns. ”What sport do you play?” Sport People Soccer 100 Tennis 45 Gymnas 55 Swimming 80

27. Simple Table Data relating to only one characteristics Gender No of Students Boys 10 Girls 20

28. Double Table Data relating to only 2 characteristics Gender Food Habit Healthy food Non healthy food Boys 3 7 Girls 5 15

29. Frequency Table Method of organizing raw data in a compact form by displaying the characteristics and frequencies. Can be used for quantitative (numerical data) and qualitative data (categorical data). For quantitative, there are two type of table, ie : grouped and ungrouped table

30. Construct Frequency Table Participant ages at retirement n = 32 lower class limit of first class – 48 No of classes = Class width = range/ no of class = (74-48)/6= 4.33~5   56 58 62 62 69 48 70 71 72 56 51 65 64 59 60 61 49 65 66 58 62 67 59 62 64 63 48 54 74 55 70 52

31. Fill in the blank Class Interval Frequency Class Limit Cumulated frequency Relative frequency

32. Histogram A graphical display of data using bars of different heights. Displays the shape and spread of numerical data.

33. Bar Graph Graphical representation that used bars to compare data among categories. Can be plotted vertically or horizontally Difference between histogram and bar graph histogram represent continuous variable, bar graph is for discrete variables. Histogram present numerical data, bar graph for categorical data No gap between the bars for histogram, there are gaps between bars in bar graph.

34. Frequency Polygon A graphical form of representation of data Used to depict the shape of the data and trends. Usually drawn with the help of a histogram but can be drawn without it as well.

35. Ogive Cumulative histogram that can be used to determine how many data values lies above or below a particular value in a data set. Is calculated from a frequency table by adding each frequency to the total of frequencies. There are two type of ogive More than ogive Less than ogive

36. Pie Chart Circular statistical graph which divide into slices to illustrate numerical proportion. Usually represent percentage or proportion or by angle for each category

37. Stem and Leaf A table used to display data. Stem is on the left displays the first digit Leaf is on the right and display last digit Is used to presenting quantitative data to visualize the distribution.

38. THANK YOU