Elementary Statistics BSC211 Chapter 1 PDF

Chapter 1 Elementary Statistics BSC211 Data and Statistics Chapter 1 Data and statistics 1.1 Introduction Statistics is the science of methods and theories that is used for collecting, organizing, analyzing and interpreting data to assi...

Chapter 1 Elementary Statistics BSC211 Data and Statistics Chapter 1 Data and statistics 1.1 Introduction Statistics is the science of methods and theories that is used for collecting, organizing, analyzing and interpreting data to assist in making decision in the case of uncertain topics. The origin of statistics goes back to 1663. Its mathematical foundations were laid in the 17th century with the development of probability theory. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and the natural and social sciences. Dr. Omar M. Sallah Email [email protected] 1 Chapter 1 Elementary Statistics BSC211 Data and Statistics LEARNING OBJECTIVES When you have completed this chapter, you will be able to: LO1-1 Explain why knowledge of statistics is important. LO1-2 Define statistics and provide an example of how statistics is applied. LO1-3 Differentiate between descriptive and inferential statistics. LO1-4 Classify variables as qualitative or quantitative, and discrete or continuous. LO1-5 Distinguish between nominal, ordinal, interval, and ratio levels of measurement. 1.2 Importance of statistics Knowledge of statistics is important in every field of life because 1- It is an easy job to collect data from field, since data are everywhere. 2- Statistical techniques could be used to make many decisions that affect in our life. 3- All of our future work will depend on decisions that involve data. 1.3 Statistical steps Stages of statistics can be summarized, briefly as: 1- Collecting data. 2- Displaying this data. 2- Populating the displayed data. 4- Analyzing and decision-making. Dr. Omar M. Sallah Email [email protected] 2 Chapter 1 Elementary Statistics BSC211 Data and Statistics 1.4 Classification of statistics One of the very famous classifications of statistics is the natural classification where statistics can fall in the following classifications 1.4.1 Descriptive statistics Concerned with the methods of organizing, summarizing and representation of data and sampling meaning Displaying data: 1- Graphical displaying. 2- Histo-diagram. 3- Frequency polygon 4- Line chart 5- Bar chart Calculation of measures Measures of location: 1- Arithmetic mean 2- Median 3- Mode 4- Harmonicity Measures of dispersions 1- Range. 2- Variance. Dr. Omar M. Sallah Email [email protected] 3 Chapter 1 Elementary Statistics BSC211 Data and Statistics 3- Standard deviation. 4- Deviation. 5- Median deviation. 6- Inter-quartile deviation. Coefficient of kurtosis and skewness Correlation and regression coefficient 1.4.2 Inferential statistics Concerned with the methods used to determine the various measures of population depending on the reached measures of samples. Sample results  Inferentia  Population aimed results  l statistics 1.4.3 Exploratory data analysis EDA is an approach to analyze data for the purpose of formulating hypotheses worth testing, complementing the tools of conventional statistics for testing hypotheses. EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task. 1.5 Population and sample Population is the whole universe of all possible individual objects or measures of interest. Sample is a subset of the population where observations are actually made. Dr. Omar M. Sallah Email [email protected] 4 Chapter 1 Elementary Statistics BSC211 Data and Statistics  Sample statistics   Population parameters       x Arithmetic mean  Inferential statistics   Pop. mean   2      2 Pop. Variance   S Variance     S S tan dard deviation    S tan d. deviation  1.6 Sampling in statistics Samples are essential in statistics as it should be representative, unbiased, etc... Sampling importance can be summarized in the following: 1- It is more economic to study any property on samples than on population, because of its small size compared to population. 2- Saving time of study. 3- It is a must in the case of infinite population. 4- It is also necessary in case of inaccessible population. 5- In case of destructive population. We have no other way to study but samples. 6- More describable when the population size huge. 1.7 Stages of statistical sampling 1- Planning stage: the study's design is established and the procedure is chosen. 2- Data collocation stage: the actual work of getting observations by measuring or counting. Dr. Omar M. Sallah Email [email protected] 5 Chapter 1 Elementary Statistics BSC211 Data and Statistics 3- Data analyzing stage: where the descriptive and inferential statistics are used. 1.8 Main types of samples Samples could be classified to: 1- The convenience sample, where the simplest and easiest observation is made. 2- The judgment sample, practical sample units are chosen to guarantee a representative sample. 3- The random sample, here all units of community has equal chances to be selected in the sample. 4- Consecutive sampling, involve every selection criteria in community. 1.9 Data and statistics In statistics data sets usually come from actual observations obtained by sampling a statistical population, and each row corresponds to the observations on one element of that population. Data sets may further be generated by algorithms for the purpose of testing certain kinds of software. 1.10 Classification of Data Data could be classified to two main categories Dr. Omar M. Sallah Email [email protected] 6 Chapter 1 Elementary Statistics BSC211 Data and Statistics a)- Qualitative data, used when a non-numerical characteristic being studied. The level of measurement used with this type of data is the nominal or ordinal level of data. b)- Quantitative data, used when a characteristic studied can be reported numerically. The numerical characteristic is always referred to a variable. The level of measurement used with this type of data is the interval and ratio level of data. 1.11 Important definitions: I- Mutually exclusive, an individual or object is included in only one category. Also, can be defined, as the appearance of an event will prevent the appearance of other events. II- Every individual or object must appear in a specified category. Dr. Omar M. Sallah Email [email protected] 7 Chapter 1 Elementary Statistics BSC211 Data and Statistics 1.12 Nature of variables used with quantitative variables The variables used are either continuous or discrete data:- 1)- Discrete Variable, can assume only certain values and there are usually gaps between the values. For example, number of employs in a certain number of departments. 2)- Continuous variable, can assume any value within a specific range. For example, like weight of shipment, miles driven between oil changes, temperature, etc. 1.13 Levels of measurements Data can be classified according to their level of measurement. The level of measurement determines how data should be summarized and presented. It also will indicate the type of statistical analysis that can be performed. 1)-Nominal level of data Here the observations can only be classified or counted. There is no particular order to the labels. Example, the color of gummy balls in a sweet jar red, yellow, blue, green,..etc. The classification of the six colors of M&M milk chocolate candies is an example, of the nominal level of measurement. Summary of the nominal data properties: Dr. Omar M. Sallah Email [email protected] 8 Chapter 1 Elementary Statistics BSC211 Data and Statistics 1- Data categories are mutually exclusive and exhaustive. So, an object belongs to one and only one category. 2- Data categories have no logical order. 2)-Ordinal level data Data recorded at the ordinal level of measurement are based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked or counted. Data are being ordered from the higher to the lowest. In summary the properties of the ordinal level data is: 1- Data categories are mutually exclusive and exhaustive. 2- Data categories are ranked or ordered according to the particular trial they possess. 3)-Interval level data Here data are ordered in intervals with constant width. For data recorded at the interval level of measurement, the interval or the distance between values is meaningful. The interval level of measurement is based on a scale with a known unit of measurement. Properties are: 1- Data categories are mutually exclusive and exhaustive. 2- Data categories are scaled according to the amount of the characteristic they possess. Dr. Omar M. Sallah Email [email protected] 9 Chapter 1 Elementary Statistics BSC211 Data and Statistics 3- Equal differences in the characteristic are represented by equal difference in the numbers assigned to the categories. 4)- Ratio level data The ratio level is the highest level of measurements. It has the same properties as the previous but with addition to the zero point. Data recorded at the ratio level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale. Properties are: 1- Data categories are mutually exclusive and exhaustive. 2- Data categories are scaled according to the amount of the characteristic they possess. 3- Equal differences in the characteristic are represented by equal difference in the numbers assigned to the categories. 4-The zero point reflects the absence of the characteristic. Dr. Omar M. Sallah Email [email protected] 10 Chapter 1 Elementary Statistics BSC211 Data and Statistics Dr. Omar M. Sallah Email [email protected] 11 Chapter 1 Elementary Statistics BSC211 Data and Statistics Exercise (1) Report (1) will be required after one week. This page must be attached to the report Name: Report Code ( ) 1)- give a suitable definition for - Inferential statistics- Ratio level data- Mutually exclusive- Stages of statistical sampling 2) -What is the difference between discrete and continuous variable? 3) - What is the meaning of mutually exclusive events give examples? 4) - Define Qualitative data and Quantitative data? 5) - What is the importance of statistics? 6) - What are the main steps of statistics? 7) - what is the importance of sampling? 8. Explain the difference between a sample and a population. 9. Explain the difference between a discrete and a continuous variable. Give an example of each not included in the text. Dr. Omar M. Sallah Email [email protected] 12 Chapter 1 Elementary Statistics BSC211 Data and Statistics 10. For the following situations, would you collect information using a sample or a population? Why? a. Statistics 201 is a course taught at a university. Professor Rauch has taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course. b. As part of a research project, you need to report the average profit as a percentage of revenue for the #1-ranked corporation in the Fortune 500 for each of the last 10 years. c. You are looking forward to graduation and your first job as a salesperson for one of five large pharmaceutical corporations. Planning for your interviews, you will need to know about each company’s mission, profitability, products, and markets. d. You are shopping for a new MP3 music player such as the Apple iPod. The manufacturers advertise the number of music tracks that can be stored in the memory. Usually, the advertisers assume relatively short, popular songs to estimate the number of tracks that can be stored. You, however, like Broadway musical tunes and they are much longer. You would like to estimate how many Broadway tunes will fit on your MP3 player. 11. Exits along interstate highways were formerly numbered successively from the western or southern border of a state. However, the Department of Transportation has recently changed most of them to agree with the numbers on the mile markers along the highway. a. What level of measurement were data on the consecutive exit numbers? b. What level of measurement are data on the milepost numbers? c. Discuss the advantages of the newer system. Dr. Omar M. Sallah Email [email protected] 13