Business Statistics PDF

Review ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 1 Learning Outcomes Outcome 1. Know the key data collection methods. Outcome 2. Know the difference between a population and a sample. Outcome 3. Understand the similarities and differences between different sa...

Review ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 1 Learning Outcomes Outcome 1. Know the key data collection methods. Outcome 2. Know the difference between a population and a sample. Outcome 3. Understand the similarities and differences between different sampling methods. Outcome 4. Understand how to categorize data by type and level of measurement. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 2 1.1 What is Business Statistics? A collection of procedures and techniques used to convert data into meaningful information in a business environment ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 3 Data Variables Observations ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 4 Statistical Procedures Descriptive Statistics – Procedures and techniques designed to describe data Inferential Statistics – Tools and techniques that help decision makers to draw inferences from a set of data ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 5 Descriptive Procedures Charts, graphs, and tables Numerical measures N x i Sum of all data values Average  i 1  N Number of data values ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 6 Inferential Procedures Estimation – e.g., Estimate the average family income of all families in a city based on the average income of a sample of families in that city. Hypothesis Testing – e.g., Use sample evidence to test the claim that the average family income exceeds $45,000 per year. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 7 1.2 Procedures for Collecting Data Data Collection Techniques Experiments Telephone surveys Written questionnaires and surveys Direct observation and personal interview ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 8 Data Collection Techniques ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 9 Other Data Collection Techniques Focus Groups Documents and Records – Studying existing data (secondary data) contained in databases, financial records, annual reports, etc. – Potentially less expensive than generating primary data but may not be complete. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 10 1.3 Populations, Samples, and Sampling Techniques Population – The set of all objects or individuals of interest. or the measurements obtained from all objects or individuals of interest Sample – A subset of the population Census – An enumeration of the entire set of measurements taken from the whole population ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 11 Population vs. Sample Population Sample a b c d b c e f g h i j k l m n g h k l m n o p q r s t u v o r s v w x y z w z A Subset of the Customers All Customers in the Market Area ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 12 Parameters Parameters – Descriptive numerical measures, such as an average or a proportion, that are computed from an entire population Examples: The average yards gained per play by all NFL teams in the 2016 season The proportion of all university students in California who have more than $40,000 in student loans ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 13 Statistics Statistics – Descriptive numerical measures, such as an average or a proportion, that are computed from a sample selected from a population. Examples: The average credits taken by a sample of students at a university. The proportion of defective parts in a sample of parts selected from the parts made by a automotive supply company. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 14 Sampling Techniques Statistical – Sampling methods that use selection techniques based on chance selection Nonstatistical – Methods of selecting samples that use convenience, judgment, or other non-chance processes ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 15 Sampling Techniques Sampling Techniques Nonstatistical Sampling Statistical Sampling Convenience Judgment Ratio Simple Systematic Random Stratified Cluster ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 16 Statistical Sampling Items of the sample are chosen based on known or calculable probabilities. Statistical Sampling (Probability Sampling) Simple Random Stratified Systematic Cluster ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 17 Statistical Sampling Also called probability (or random) sampling Allows every item in the population to have a known or calculable chance of being included in the sample ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 18 Simple Random Sampling Every possible sample of a given size has an equal chance of being selected Selection may be with replacement or without replacement The sample can be obtained using a table of random numbers or computer random number generator ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 19 Sampling Methods - Summary ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 20 1.4 Data Types and Data Measurement Levels The starting point in analyzing data is to know what kind of data you have collected. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 21 Data Types Quantitative: – measurements whose values are inherently numerical discrete (e.g. number of children) continuous (e.g. weight, volume) Qualitative: – data whose measurement scale is inherently categorical (e.g. marital status, political affiliation, eye color) ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 22 Data Types Time-Series: – a set of consecutive data values observed at successive points in time (e.g. stock price on daily basis for a year) Cross-Sectional: – A set of data values observed at a fixed point in time (e.g. bank data about its loan customers) ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 23 Data Timing Example Sales (in $1000s) 2009 2010 2011 2012 Time Series Atlanta 435 460 475 490 Data Boston 320 345 375 395 Cleveland 405 390 410 395 Denver 260 270 285 280 Cross Sectional Data ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 24 Data Types and Data Measurement Levels - Summary ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 25 Transforming Data to Information Information Data Statistical Tools ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 26 A Typical Application Sequence Decide on Statistical or Determine a Need for Data Nonstatistical Sampling Determine Data Types and Define the Population Measurement Level Determine What Data You Select Graphic Presentation Will Need Tools Decide How the Data Will Be Compute Numerical Collected Measures Decide on a Census or a Write the Statistical Report Sample ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 27 A Typical Application Sequence Step 1: Determine a Need for Data: – Research the issue – Analyze business alternatives – Respond to request for information Step 2: Define the Population: – All items of interest – Determine how to gain access to the population ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 28 A Typical Application Sequence Step 3: Determine What Data You Will Need: – Identify the key variables – What categorical breakdowns will be needed? Step 4: Decide How the Data Will Be Collected: – Experiment – Observation – Automation – Telephone Survey – Written Survey – Personal Interview ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 29 Data Types and Measurement Level Step 5: Decide on a Census or a Sample: – Census: All items in the population – Sample: A subset of the population Step 6: Decide on Statistical or Nonstatistical Sampling: – Statistical Sampling: Simple Random Sample Stratified Random Sample Systematic Random Sample Cluster Random Sample – Non-statistical Sampling: Convenience Sampling Judgment Sampling ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 30 Data Types and Measurement Level Step 7: Determine Data Types and Measurement Level: The methods of descriptive statistical analysis that can be performed depends on the type of data and the level of data measurement for the variables in the data set. Step 8: Select Graph Presentation Tools: Quantitative Qualitative Frequency Cross-sectional Time series distribution Frequency Bar Chart Line Chart Distribution Pie chart Histogram Par Chart ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 31 Data Types and Measurement Level Step 9: Compute Numerical Measure: Range Median Variation Types of Central Location Interquartile Measures Mean Range Descriptive Mode Variance and Standard analysis & Percentiles Deviation comparisons Quartile Percentiles Coefficient of Quartile Variation Box and Standardized Whisker Z - values ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 32 Data Types and Measurement Level Step 10: Write the Statistical Report: There is no one set format for writing a statistical report. However, there are a few suggestions you may find useful. - Lay the foundation; provide background and motivation for the analysis. - Describe the data collection methodology; Explain how the data were generated and the sampling techniques were used. - Use s logical sequence; follow a systematic plan for presenting your findings and analysis. - Label figures and tables by number; employ consistent numbering and labeling format. ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 33 Describing data using numerical measures. 1- Measures of Center Population Mean - Example Each day, a local hospital counts the number of patients that are in the hospital. This is called the hospital census. The hospital is interested in only the census data for the past 10 days. This is the population of interest. The data are shown below: 216 255 330 254 348 317 292 267 310 295   x i = 216 + 255 + 330 +..... 10 310 + 295 = 2,884 = 288.4 10 N ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 34 Median The median is a center value that divides a data array into two halves (Md). Data Array – Data that have been arranged in numerical order Median Index – i = The index of the point in the data set corresponding to the median value – n = Sample size ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 35 Mode The mode is the value in the data that occurs most frequently ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 36 2- Measures of Variation Range – Simple range – Interquartile Range Variance Standard Deviation Coefficient of Variation ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 37 Range A measure of variation that is computed by finding the difference between the maximum and minimum values in a data set Simplest measure of variation Is very sensitive to extreme values Ignores the data distribution ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 38 Population Variance The average of the squared distances of the data values from the mean xi216 Xi-𝜇 … (Xi-𝜇) … 2 255 … … 330 … …  ( xi   ) N 2 254 … … 348 … …  317 … …  2 i 1 292 … … N 310 … … 295 …. …. µ - population mean, N – population size ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 39 Population Standard Deviation The most commonly used measure of variation The positive square root of the variance  ( xi   ) N 2   2  i 1 N Has the same units as the original data ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 40 Coefficient of Variation Is used to compare two or more sets of data measured in different units Population CV  CV  (100)%  Where: 𝜎 = population standard deviation and 𝜇 = population mean Sample CV s CV  (100)% x Where: 𝑠 = sample standard deviation and 𝑥 = sample mean ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. Slide - 41 Standardized Data Values The number of standard deviations a value is from the mean. Standardized data values are also referred to as z scores. x x – original data value Population z score z  µ - population  mean σ – population standard Sample z score z xx deviation 𝑥 – sample mean s s – sample standard deviation ALWAYS LEARNING Copyright © 2018 Pearson Education, Ltd. 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