QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
Chapter 1 Data and Statistics Descriptive
Statistics
Business Statistics: Collection, Summarization, analysis, reporting of numerical findings relevant to a business decision
Inferential
Qualitative/Categ orical Discrete
Variables Quantitative
Continuous
Nominal
Scale Ordinal
Interval
Ratio
1
Sample v.s Population
QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
1. Introduction 1. What is the definition for business statistics? 2. Statistics 1. Can you judge a statistics is a descriptive or inferential statistics? 2. Population characterized by parameter, but sample characterized by statistics (table on slide) 3. Variables 1. Judge a variable is qualitative or quantitative variable 4. Scales 1. The difference between nominal and ordinal scale. 2. The difference between interval and ratio scale.
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QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
Chapter 2 Visual Description
Relative
Frequency Distribution
Quantitative
One variable
Histogram
Cumulative
Relative cumulative
Stem-‐and-‐ leaf Display
Two variables association
Scatter Diagram
Cross/ Contingency table
Raw data
Data array
Relative
Categorical
One variable
Frequency Distribution
Cumulative
Pie Chart
Relative cumulative
Bar Chart
Two variables association
3
Cross/ Contingency table
QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
2 Frequency distribution 1. How to find class interval and class mark? 2. Find any dataset and draw table like Table 2.2. It will be a helpful practice. 3. The two important characteristics for histogram: no gap (adjacent) and the length proportional to frequency. 4. you need to know how it relates to class mark. 3 Stem-‐and-‐leaf display and 1. For the stem-‐and-‐leaf display, you need to choose difference and proper digit (unit) 4 Other methods
1. Bar chart: differences between bar chart and histogram (1. Type of variable; 2.adjacent?) 5 scatter diagram 1. Can you draw diagram to show direct, inverse, direct curvilinear, reverse curvilinear and no relationship? 6 Tabulation 1. it is for qualitative variable and two types: simple and cross. *Skills: Use excel to draw frequency distribution, histogram and scatter diagram with tendency line
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QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
Chapter 3 Statistical Description Mean Median Central/ location
Mode Geometric Mean Weighted M ean Range
Variance
Measurement
Dispersion / Variability
Std. Deviation Mean Absolute Deviation (MAD)
Coefficient of Variation (CV) Skewness Shape of distribution Association of 2 variables
Symmetric/Positivel y/ Negatively Skewed Distribution
Relative Position of mean and median Coefficient of Correlation Covariance
Find Outliers
Z-‐score
5
Larger than 3 or smaller than -‐3
QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
1. Statistical description: Measures of central tendency/location *This chapter you need to know the difference between sample and population statistics. 1. (Arithmetic) Mean: the differences between sample and pollution mean 2. The weakness of mean is from the influential outliers. 3. How to find the weighted mean (the arithmetic mean is the special case of weighted mean, which sets the weight equal to 1) 4. Median: the number of observation makes the calculation difference. (Odd number and even number) 5. Median will not be affected by influential outliers 6. Mode: how to find the mode? We can have more than one mode. 7. The difference among mean, median and mode 8. Can you find relative position of mean, median and mode for symmetrical, skewed distribution? 9. how to apply the weighted mean to calculate the trade-‐weighted exchange rate 10. how to apply the geometric mean to calculate the growth rate 2. Statistical description: measures of dispersion/ variability 1. Range: Two ways to express it 2. The weakness for range 3. Calculate the variance, standard deviation 4. MAD: how to calculate it 5. How to standardize data? 𝑧! =
!!! !
for sample or 𝑧! =
!!! !
for population
6. How to calculate the coefficient of variation? It explains how much varies relative to its average. 3 statistical measures of association 1. Coefficient of correlation: how it reflect the direction and strength of the linear relationship? What is the range for it?
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QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
2. Coefficient of determination: how to get it from coefficient of correlation? What is the range of it? You can interpret it as how many percentages of variation in dependent variable is explained by independent variable. *Skills: Use excel to get mean, standard deviation, standard value
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QUAN340
Keynotes (chap1-‐6)
Chapter 4 Introduction of probability Review Homework 3 on CengageNOW.
8
Dr. Jingze Jiang
QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
Chapter 5: Discrete Probability Distribution 1 Introduction 1. The definition for discrete random variable and continuous random variable. (Blue box in textbook) 2. 2 Properties of a discrete probability distribution. 3. General methods for the mean and variance of a discrete probability distribution. 2 Binomial distribution 1. Characteristics of Binomial distribution (check slides) 2. Probability distribution for Binomial distribution, mean, variance 3. Which sampling will keep the probability same, with or without replacement? Binomial belongs to sampling with or without replacement?
9
QUAN340
Keynotes (chap1-‐6)
Dr. Jingze Jiang
Chapter 6: Continuous Probability Distribution 1 Introduction 1. Properties of a continuous probability distribution. (Blue box in textbook) 2 Normal distribution 1. Probability distribution for normal distribution, mean, variance 2. Symmetric, and bell-‐shaped distribution, with mean=mode=median 3. How the density distribution will change, if we increase 𝝁? (move right) 4. How the density distribution will change, if we increase 𝝈? (Fat= eating more ^-‐^ ! larger dispersion ) 5. The application of empirical rule: 1 standard deviation, 2 standard deviations, 3 standard deviations 3 Standard Normal distribution 1. The characteristics of standard normal distribution: mean zero, standard deviation 1 2. How to standardize date? Can you find the probability for a given z value from Standard Normal Distribution Table? e.g.: 𝜎 = 10, 𝜇 = 100 The probability for 𝑥 ≤ 120? 𝑧 =
!"#!!""
The probability for 𝑥 > 140? 𝑧 =
!"#!!""
!"
!"
= 2, check the table z=2 and find the probability = 4, check the table z=4 and find the probability 𝑃 𝑋 ≤
140 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑤ℎ𝑒𝑛 𝑧 = 4, then 1 − 𝑃 𝑋 ≤ 140 = 𝑃 𝑋 > 140
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