Introduction to Statistics

Transcription

1 Introduction to Statistics Sherif Khalifa Sherif Khalifa () Introduction to Statistics 1 / 36

2 Every day businesses make decisions that determine whether companies will be profitable and flourish or whether they will stagnate and die. These decisions are made with the assistance of information gathered on the market place, the economy, the workforce, the competition, and the financial environment. Such information usually comes in the form of data, or is accompanied by data. Business statistics provide the tool through which such data are collected, analyzed, summarized, and presented to facilitate the decision making process. Sherif Khalifa () Introduction to Statistics 2 / 36

3 Examples the demand for related products, consumer satisfaction with the product, the quality of the product, the advertising effectiveness, stock prices in financial markets, the intensity of competition in the market, customer demand by age group, customer demand by income group, the unemployment in the labor market, the skill abundance in the labor market, changes to workplace to improve productivity, the customer opinion on environmental issues. Sherif Khalifa () Introduction to Statistics 3 / 36

4 Statistics is the science of dealing with the collection, analysis, interpretation, and presentation of numerical data. Sherif Khalifa () Introduction to Statistics 4 / 36

5 A population is a collection of persons, objects, or items of interest. Examples Population of the United States, Population in California, voters in Orange County, All automobiles in the country, All Ford Mustang cars produced this decade, All workers presently employed by Microsoft, All dishwashers produced by General Electric this year. A census is the data collected from the whole population for a given measurement of interest. Examples The United States Census. Every 10 years the United States government attempts to measure all persons living in the country. Sherif Khalifa () Introduction to Statistics 5 / 36

6 A sample is a portion of the whole, gathering data on a subset of the population. If a sample is properly taken, it is representative of the whole. Researchers prefer to work with samples rather than with the entire population because of time and money limitations. Sherif Khalifa () Introduction to Statistics 6 / 36

7 Descriptive statistics is using data gathered on a group to describe or reach conclusion about the same group. Examples Number of employees in vacation in the Summer this year, Average salary of wokers in a certain company, Corporate sales of a firm in a certain year. Sherif Khalifa () Introduction to Statistics 7 / 36

8 Inferential statistics is gathering data from a sample and using the statistics generated to reach conclusions about the population from which the sample was taken. The data gathered from the sample is used to infer something about a larger group. The advantage of inferential statistics is that they enable the researcher to study effectively a wide range of phenomenona without having to conduct a census. Sherif Khalifa () Introduction to Statistics 8 / 36

9 A parameter is a descriptive measure of the population. µ : population mean σ 2 : population variance σ : population standard deviation A statistic is a descriptive measure of the sample. x : sample mean s 2 : sample variance s : sample standard deviation Sherif Khalifa () Introduction to Statistics 9 / 36

10 A business researcher wants to estimate the value of a parameter, or conduct tests about the parameter. The calculation of the parameters is usually either impossible of infeasible because of the amount of time and money required to take a census. The business researcher can take a random sample of the population, caculate a statistic on the sample, and infer by estimation the value of the parameter. Inferential statistics is the ability to make decisions about parameters without having to complete a census of the population Sherif Khalifa () Introduction to Statistics 10 / 36

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12 A variable is a characteristic of any entity being studied that is capable of taking on different values. A measurement is when a standard process is used to assign numbers to particular attributes or characteristics of a variable. Data are recorded measurements. Sherif Khalifa () Introduction to Statistics 12 / 36

13 The process of measuring and data gathering are basic to all that we do in business statistics. It is data that are analysed by a business statistician in order to learn more about the variables being studied. All such data should not be analyzed the same way statistically because the entities represented by the numbers are diffferent. The business researcher needs to know the level of data measurement represented by the numbers being analyzed. Sherif Khalifa () Introduction to Statistics 13 / 36

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15 The lowest level of data measurement is the nominal level. Numbers representing nominal level data can be used to classify or categorize. No order of the cases is implied. Examples employment, sex, religion, ethnicity, geographic location, place of birth, social security number, telephone number, ID number, Zip code. Numbers are used to classify or categorize Example: Employment Classification 1 for Educator 2 for Construction Worker 3 for Manufacturing Worker Sherif Khalifa () Introduction to Statistics 15 / 36

16 Ordinal level data can be used to rank or order people or objects. With ordinal data, the distance or spacing represented by consecutive numbers are not always equal. Strongly Agree Agree Neutral Disagree Strongly Disagree Sherif Khalifa () Introduction to Statistics 16 / 36

17 Interval level data is the next to the highest level of data in which the distances between consecutive numbers have meaning and the data are always numerical. Examples Fahrenheit temperature, percentage change in employment, percentage return on a stock, the change in stock prices. Sherif Khalifa () Introduction to Statistics 17 / 36

18 Ratio level data is the highest level of data measurement, and have the same properties as interval data but ratio data have an absolute zero and the ratio of two numbers is meaningful. Examples height, weight, time, volume, production cycle time, passenger miles, number of employees. Sherif Khalifa () Introduction to Statistics 18 / 36

19 The Senior Executive at Memorial Hospital is exploring the usage of nursing over-time hours in the emergency department during the last operating year. He intends to survey the emergency department nurses regarding their perception of over-time needs. For this survey the set of all emergency department nurses who worked at Memorial Hospital during the last operating year is: a) a parameter b) a sample c) the population d) a statistic Sherif Khalifa () Introduction to Statistics 19 / 36

20 The Senior Executive at Memorial Hospital is exploring the usage of nursing overtime in the emergency department during the last operating yeadr. Staffi ng records and emergency department visits for 30 days between the period of January 1, 2016 and December 31, 2016 are selected for analysis. For this study, the group of 30 days is a: a) parameter b) sample c) population d) statistic Sherif Khalifa () Introduction to Statistics 20 / 36

21 The Senior Executive at Memorial Hospital is exploring the usage of nursing overtime in the emergency department during the last operating year. Staffi ng records and emergency department visits for all 365 days between the period of January 1, 2016 and December 31, 2016 are selected for analysis. The dataset can best be classified as a: a) statistic b) census c) sample d) parameter Sherif Khalifa () Introduction to Statistics 21 / 36

22 Some of the most effective mechanisms for presenting data in a form meaningful to decision makers are graphical depictions. Through graphs, decision maker can often get an overall picture of the data and reach some useful conclusions by studying the chart. Visual representations of data are often much more effective communication tools than tables of numbers. A first step in exploring data is to reduce data to a graphic picture that is clear, concise and consistent with the message of the original data. Sherif Khalifa () Introduction to Statistics 22 / 36

23 Ungrouped data is raw data that have not been summarized in any way Example of Ungrouped Data years of unemployment rates Sherif Khalifa () Introduction to Statistics 23 / 36

24 Grouped data is data that have been organized into a frequency distribution. Class Frequency Class Relative Cumulative Interval Midpoint Frequency Frequency 1-under under under under under under Sherif Khalifa () Introduction to Statistics 24 / 36

25 Frequency distribution is a summary of data presented in the form of class intervals and frequencies. Steps in Frequency Distribution Step 1 Determine range of frequency distribution Range is the difference between the high and the lowest numbers Step 2 determine the number of classes Don t use too many, or two few classes Step 3 Determine the width of the class interval Approx class width can be calculated by dividing the range by the number of classes Values fit into only one class Sherif Khalifa () Introduction to Statistics 25 / 36

26 The range is the difference between the largest and smallest numbers. The midpoint of each class interval is called the class midpoint. It is the value halfway across the class interval and can be calculated as the average of the two class endpoints. Sherif Khalifa () Introduction to Statistics 26 / 36

27 Relative frequency is the proportion of the total frequency that is in any given class interval in a frequency distribution. Relative frequency is the individual class frequency divided by the total frequency. Culmulative frequency is a running total of frequencies through the classes of a frequency distribution. The cumulative frequency for each class interval is the frequency for that class interval added to the preceding cumulative total. Sherif Khalifa () Introduction to Statistics 27 / 36

28 A histogram is a series of contiguous rectangles that represent the frequency of data in given class intervals. Class Interval Frequency 1 under under under under under under 13 5 Unemployment Data Histogram Sherif Khalifa () Introduction to Statistics 28 / 36

29 A frequency polygon is a graphical display of class frequencies. Each class frequency is plotted as a dot at the class midpoint, and the dots are connected by a series of lines. Class Interval Frequency 1 under under under under under under 13 5 Unemployment Data Frequency Polygon Sherif Khalifa () Introduction to Statistics 29 / 36

30 Ogive is a cumulative frequency polygon. Cumulative Class Interval Frequency 1 under under under under under under Unemployment Data Ogive Sherif Khalifa () Introduction to Statistics 30 / 36

31 In a dot plot, each data value is plotted along the horizontal axis and is represented on the chart by a dot. Sherif Khalifa () Introduction to Statistics 31 / 36

32 A pie chart is a circular depiction of data where the area of the whole pie represents 100% of the data and slices of the pie represent a percentage breakdown of the sublevels. Company Sales Proportion Exxon Mobil Chevron Conoco Phillips Valero Energy Total Sherif Khalifa () Introduction to Statistics 32 / 36

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34 A bar chart contains two or more categories along one axis, and a s eries of bars, one for eaxg category, along the other axis. Category Expenditure Electronics Clothing Furnishings School supplies Miscellaneous Sherif Khalifa () Introduction to Statistics 34 / 36

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36 A scatter plot is a two dimensional graph plot of pairs of points from two numerical variables. Scatter Plot Value of New Construction Over a 35 Year Period Sherif Khalifa () Introduction to Statistics 36 / 36