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business and economics statics principles
1.
Copyright © 2010
Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-1 Statistics for Business and Economics 7th Edition Chapter 1-2 Basics
2.
Dealing with Uncertainty Everyday
decisions are based on incomplete information Consider: Will the job market be strong when I graduate? Will the price of Yahoo stock be higher in six months than it is now? Will interest rates remain low for the rest of the year if the budget deficit is as high as predicted? Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-2 1.1
3.
Dealing with Uncertainty Numbers
and data are used to assist decision making Statistics is a tool to help process, summarize, analyze, and interpret data Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-3 (continued)
4.
Key Definitions A
population is the collection of all items of interest or under investigation N represents the population size A sample is an observed subset of the population n represents the sample size A parameter is a specific characteristic of a population A statistic is a specific characteristic of a sample Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-4 1.2
5.
Population vs. Sample Copyright
© 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-5 a b c d ef gh i jk l m n o p q rs t u v w x y z Population Sample Values calculated using population data are called parameters Values computed from sample data are called statistics b c g i n o r u y
6.
Examples of Populations
Names of all registered voters in Turkey Incomes of all families living in Hawai Annual returns of all stocks traded on the New York Stock Exchange Grade point averages of all the students in your university Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-6
7.
Random Sampling Simple random
sampling is a procedure in which each member of the population is chosen strictly by chance, each member of the population is equally likely to be chosen, every possible sample of n objects is equally likely to be chosen The resulting sample is called a random sample Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-7
8.
Descriptive and Inferential
Statistics Two branches of statistics: Descriptive statistics Graphical and numerical procedures to summarize and process data Inferential statistics Using data to make predictions, forecasts, and estimates to assist decision making Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-8
9.
Descriptive Statistics Collect
data e.g., Survey Present data e.g., Tables and graphs Summarize data e.g., Sample mean = Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-9 i X n
10.
Inferential Statistics Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-10 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 140 pounds Inference is the process of drawing conclusions or making decisions about a population based on sample results
11.
Types of Data Data Categorical
Numerical Discrete Continuous Examples: Marital Status Are you registered to vote? Eye Color (Defined categories or groups) Examples: Number of Children Defects per hour (Counted items) Examples: Weight Voltage (Measured characteristics) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 1-11
12.
Describing Data Numerically Copyright
© 2010 Pearson Education, Inc. Publishing as Prentice Hall Arithmetic Mean Median Mode Describing Data Numerically Variance Standard Deviation Coefficient of Variation Range Interquartile Range Central Tendency Variation Ch. 2-12
13.
Measures of Central
Tendency Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Central Tendency Mean Median Mode n x x n 1 i i Overview Midpoint of ranked values Most frequently observed value Arithmetic average Ch. 2-13 2.1
14.
Arithmetic Mean The
arithmetic mean (mean) is the most common measure of central tendency For a population of N values: For a sample of size n: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Sample size n x x x n x x n 2 1 n 1 i i Observed values N x x x N x μ N 2 1 N 1 i i Population size Population values Ch. 2-14
15.
Arithmetic Mean The
most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall (continued) 0 1 2 3 4 5 6 7 8 9 10 Mean = 3 0 1 2 3 4 5 6 7 8 9 10 Mean = 4 3 5 15 5 5 4 3 2 1 4 5 20 5 10 4 3 2 1 Ch. 2-15
16.
Median In an
ordered list, the median is the “middle” number (50% above, 50% below) Not affected by extreme values Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3 Ch. 2-16
17.
Finding the Median
The location of the median: If the number of values is odd, the median is the middle number If the number of values is even, the median is the average of the two middle numbers Note that is not the value of the median, only the position of the median in the ranked data Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall data ordered the in position 2 1 n position Median 2 1 n Ch. 2-17
18.
Mode A measure
of central tendency Value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may may be no mode There may be several modes Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 0 1 2 3 4 5 6 No Mode Ch. 2-18
19.
Review Example Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Five houses on a hill by the beach $2,000 K $500 K $300 K $100 K $100 K House Prices: $2,000,000 500,000 300,000 100,000 100,000 Ch. 2-19
20.
Review Example: Summary Statistics Copyright
© 2010 Pearson Education, Inc. Publishing as Prentice Hall Mean: ($3,000,000/5) = $600,000 Median: middle value of ranked data = $300,000 Mode: most frequent value = $100,000 House Prices: $2,000,000 500,000 300,000 100,000 100,000 Sum 3,000,000 Ch. 2-20
21.
Which measure of
location is the “best”? Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Mean is generally used, unless extreme values (outliers) exist . . . Then median is often used, since the median is not sensitive to extreme values. Example: Median home prices may be reported for a region – less sensitive to outliers Ch. 2-21
22.
Measures of Variability Copyright
© 2010 Pearson Education, Inc. Publishing as Prentice Hall Same center, different variation Variation Variance Standard Deviation Coefficient of Variation Range Interquartile Range Measures of variation give information on the spread or variability of the data values. Ch. 2-22 2.2
23.
Range Simplest measure
of variation Difference between the largest and the smallest observations: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Range = Xlargest – Xsmallest 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Range = 14 - 1 = 13 Example: Ch. 2-23
24.
Disadvantages of the
Range Ignores the way in which data are distributed Sensitive to outliers Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 7 8 9 10 11 12 Range = 12 - 7 = 5 7 8 9 10 11 12 Range = 12 - 7 = 5 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,5 1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,120 Range = 5 - 1 = 4 Range = 120 - 1 = 119 Ch. 2-24
25.
Interquartile Range Can
eliminate some outlier problems by using the interquartile range Eliminate high- and low-valued observations and calculate the range of the middle 50% of the data Interquartile range = 3rd quartile – 1st quartile IQR = Q3 – Q1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-25
26.
Interquartile Range Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Median (Q2) X maximum X minimum Q1 Q3 Example: 25% 25% 25% 25% 12 30 45 57 70 Interquartile range = 57 – 30 = 27 Ch. 2-26
27.
Population Variance Average
of squared deviations of values from the mean Population variance: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall N μ) (x σ N 1 i 2 i 2 Where = population mean N = population size xi = ith value of the variable x μ Ch. 2-27
28.
Sample Variance Average
(approximately) of squared deviations of values from the mean Sample variance: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 - n ) x (x s n 1 i 2 i 2 Where = arithmetic mean n = sample size Xi = ith value of the variable X X Ch. 2-28
29.
Population Standard Deviation
Most commonly used measure of variation Shows variation about the mean Has the same units as the original data Population standard deviation: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall N μ) (x σ N 1 i 2 i Ch. 2-29
30.
Sample Standard Deviation
Most commonly used measure of variation Shows variation about the mean Has the same units as the original data Sample standard deviation: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 1 - n ) x (x S n 1 i 2 i Ch. 2-30
31.
Calculation Example: Sample Standard
Deviation Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Sample Data (xi) : 10 12 14 15 17 18 18 24 n = 8 Mean = x = 16 4.2426 7 126 1 8 16) (24 16) (14 16) (12 16) (10 1 n ) x (24 ) x (14 ) x (12 ) X (10 s 2 2 2 2 2 2 2 2 A measure of the “average” scatter around the mean Ch. 2-31
32.
Measuring variation Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Small standard deviation Large standard deviation Ch. 2-32
33.
Comparing Standard Deviations Copyright
© 2010 Pearson Education, Inc. Publishing as Prentice Hall Mean = 15.5 s = 3.338 11 12 13 14 15 16 17 18 19 20 21 11 12 13 14 15 16 17 18 19 20 21 Data B Data A Mean = 15.5 s = 0.926 11 12 13 14 15 16 17 18 19 20 21 Mean = 15.5 s = 4.570 Data C Ch. 2-33
34.
Advantages of Variance
and Standard Deviation Each value in the data set is used in the calculation Values far from the mean are given extra weight (because deviations from the mean are squared) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-34
35.
Coefficient of Variation
Measures relative variation Always in percentage (%) Shows variation relative to mean Can be used to compare two or more sets of data measured in different units Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 100% x s CV Ch. 2-35
36.
Comparing Coefficient of Variation
Stock A: Average price last year = $50 Standard deviation = $5 Stock B: Average price last year = $100 Standard deviation = $5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Both stocks have the same standard deviation, but stock B is less variable relative to its price 10% 100% $50 $5 100% x s CVA 5% 100% $100 $5 100% x s CVB Ch. 2-36
37.
Using Microsoft Excel
Descriptive Statistics can be obtained from Microsoft® Excel Select: data / data analysis / descriptive statistics Enter details in dialog box Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-37
38.
Using Excel Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Select data / data analysis / descriptive statistics Ch. 2-38
39.
Using Excel Enter
input range details Check box for summary statistics Click OK Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-39
40.
Excel output Copyright ©
2010 Pearson Education, Inc. Publishing as Prentice Hall Microsoft Excel descriptive statistics output, using the house price data: House Prices: $2,000,000 500,000 300,000 100,000 100,000 Ch. 2-40
41.
The Sample Covariance
The covariance measures the strength of the linear relationship between two variables The population covariance: The sample covariance: Only concerned with the strength of the relationship No causal effect is implied Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall N ) )(y (x y) , (x Cov N 1 i y i x i xy 1 n ) y )(y x (x s y) , (x Cov n 1 i i i xy Ch. 2-41 2.4
42.
Interpreting Covariance Covariance
between two variables: Cov(x,y) > 0 x and y tend to move in the same direction Cov(x,y) < 0 x and y tend to move in opposite directions Cov(x,y) = 0 x and y are independent Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-42
43.
Coefficient of Correlation
Measures the relative strength of the linear relationship between two variables Population correlation coefficient: Sample correlation coefficient: Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Y X s s y) , (x Cov r Y X σ σ y) , (x Cov ρ Ch. 2-43
44.
Features of Correlation Coefficient,
r Unit free Ranges between –1 and 1 The closer to –1, the stronger the negative linear relationship The closer to 1, the stronger the positive linear relationship The closer to 0, the weaker any positive linear relationship Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-44
45.
Scatter Plots of
Data with Various Correlation Coefficients Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Y X Y X Y X Y X Y X r = -1 r = -.6 r = 0 r = +.3 r = +1 Y X r = 0 Ch. 2-45
46.
Using Excel to
Find the Correlation Coefficient Select Data / Data Analysis Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Ch. 2-46 Choose Correlation from the selection menu Click OK . . .
47.
Using Excel to
Find the Correlation Coefficient Input data range and select appropriate options Click OK to get output Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall (continued) Ch. 2-47
48.
Interpreting the Result
r = .733 There is a relatively strong positive linear relationship between test score #1 and test score #2 Students who scored high on the first test tended to score high on second test Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Scatter Plot of Test Scores 70 75 80 85 90 95 100 70 75 80 85 90 95 100 Test #1 Score Test #2 Score Ch. 2-48
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